tag:blogger.com,1999:blog-72050430110982579962024-03-05T21:29:31.076+08:00SAMBIMATIKA, Concepts and Solutions of Mathematical ProblemsPembahasan tentang konsep, teknik, trik dan tips penyelesaian soal matematika untuk siswa SMP/MTs, SMA/MA/SMK/MAK dan mahasiswaNurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.comBlogger179125tag:blogger.com,1999:blog-7205043011098257996.post-47939409725295801902024-02-08T13:54:00.001+08:002024-02-09T08:44:37.341+08:00Pembahasan Soal Olympiade Matematika SD<p>Assalamualaikum sahabat guru matematika dimanapun berada,</p><p>Hari ini saya ditanya oleh anak saya beberapa sial matematika yang diberikan oleh gurunya yang katanya latihan soal olympiade. Tapi ada beberapa kendala yang saya hadapi dalam menjelaskan soal tersebut.</p><p></p><ol style="text-align: left;"><li>Saya kesulitan menjelaskan soal tersebut karena dalam penyelesaiannya sudah menggunakan variabel, sementara anak saya masih kelas IV SD belum diajarkan variabel dan saya berkesimpulan untuk menjelaskan soal ini, saya harus menambahkan pengetahuan dasar tentang variabel dan beberapa teknik penyelesaian soal dari persamaan matematika satu dan dua variabel.</li><li>Saya masih belum menemukan bahasa yang tepat menjelaskan soal ini untuk anak usia kelas IV SD, karena saya memang tidak pernah ngajar di kelas yang seusia anak SD.</li></ol>Mudahan dari tulisan singkat ini, saya bisa mendapatkan masukan dan tambahan ilmu dari bapak/ibu guru langkah yang tepat untuk menjelaskan soal-soal ini.<p></p><p>Berikut saya berikan screenshoot soal tersebut.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimqefYwAOIhMFMhNNOT-nR2DONSlvUfMkgwB9pQYjN_Lctcyrr285cpADNX9gN8X_ZVAxxhv1U-TDeHKqXVlMa3Rt9Q-7IN0iuUAOv8njRCfNI6WLM2ELQe0nGGjS2uWPcNOPXA2mOwfBOXR3WTZD7xkFVgHyEv_nlMbskWn6we5_SLLtmX49GPN9Q-lE/s1280/WhatsApp%20Image%202024-02-08%20at%2006.25.27.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1280" data-original-width="803" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimqefYwAOIhMFMhNNOT-nR2DONSlvUfMkgwB9pQYjN_Lctcyrr285cpADNX9gN8X_ZVAxxhv1U-TDeHKqXVlMa3Rt9Q-7IN0iuUAOv8njRCfNI6WLM2ELQe0nGGjS2uWPcNOPXA2mOwfBOXR3WTZD7xkFVgHyEv_nlMbskWn6we5_SLLtmX49GPN9Q-lE/w251-h400/WhatsApp%20Image%202024-02-08%20at%2006.25.27.jpeg" width="251" /></a></div><div><br /></div>Dan berikut pembahasan soalnya yang sudah saya buatkan untuk anak saya.<div><br />
<iframe src="https://drive.google.com/file/d/1zhGkd_kFSRbxVro_NgzztSyQxMXQuSdK/preview" width="640" height="480" allow="autoplay"></iframe>
<div><br /></div><div>Mohon saran dan masukannya😅</div></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0tag:blogger.com,1999:blog-7205043011098257996.post-31115919294748248212024-01-26T19:54:00.001+08:002024-01-26T19:54:11.728+08:00Kepmendikbudristek No. 262 Tahun 2022 tentang Perubahan atas Kepmendikbudristek No. 56/M/2022 tentang Pedoman Penerapan Kurikulum dalam Rangka Pemulihan Pembelajaran<p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: justify;"><span style="text-align: left;"><div class="separator" style="clear: both; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigP9AIYmbYraXJCNx-tGcl0Qg3d5H4J3Rr42fAMyurZxTtGxhVyx5c6_LzyUPF1Ix0ghpSqFkmXzKkyECTV90wGuC6mWjB31zRHAx5xYZ9j1rHBmJHRNXpmb7p7ybcdJ4_6j8J4VhRLF5JOFoE2enHhNpkcE1RmFz8dTM8bFO79eA34h-VED2Q8503Pbo/s1137/Kepmendikbud%20262%202022.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="543" data-original-width="1137" height="191" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigP9AIYmbYraXJCNx-tGcl0Qg3d5H4J3Rr42fAMyurZxTtGxhVyx5c6_LzyUPF1Ix0ghpSqFkmXzKkyECTV90wGuC6mWjB31zRHAx5xYZ9j1rHBmJHRNXpmb7p7ybcdJ4_6j8J4VhRLF5JOFoE2enHhNpkcE1RmFz8dTM8bFO79eA34h-VED2Q8503Pbo/w400-h191/Kepmendikbud%20262%202022.png" width="400" /></a></div><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: justify;"><span style="text-align: left;">Keputusan Menteri Pendidikan, Kebudayaan, Riset, dan Teknologi Republik Indonesia Nomor 262 tahun 2022 adalah peraturan yang mengubah Keputusan Menteri sebelumnya Nomor 56 tahun 2022 tentang Pedoman Penerapan Kurikulum Dalam Rangka Pemulihan Pembelajaran¹. Perubahan ini bertujuan untuk mengakomodasi minat, bakat, dan kemampuan peserta didik, serta menyesuaikan beban kerja dan penataan linieritas guru bersertifikat pendidik.</span></div></span></div></div><p></p><p style="text-align: justify;"><span style="text-align: left;">Perubahan yang dilakukan antara lain adalah:</span></p><p></p><ul style="text-align: left;"><li style="text-align: justify;">Menambahkan ketentuan tentang Projek Penguatan Profil Pelajar Pancasila (P5) sebagai salah satu kegiatan pembelajaran yang dapat dilakukan oleh peserta didik untuk mengembangkan kompetensi sikap, pengetahuan, dan keterampilan sesuai dengan minat, bakat, dan kemampuan.</li><li style="text-align: justify;">Mengubah ketentuan tentang beban kerja guru bersertifikat pendidik, yaitu minimal 24 jam tatap muka per minggu untuk guru kelas dan minimal 20 jam tatap muka per minggu untuk guru mata pelajaran.</li><li style="text-align: justify;">Mengubah ketentuan tentang penataan linieritas guru bersertifikat pendidik, yaitu guru yang mengajar di luar bidang studi atau mata pelajaran yang sesuai dengan sertifikat pendidiknya dapat mengajukan permohonan penataan linieritas kepada Kepala Dinas Pendidikan Provinsi atau Kepala Dinas Pendidikan Kabupaten/Kota.</li></ul><p></p><p style="text-align: justify;">Keputusan Menteri ini merupakan langkah positif untuk memberikan fleksibilitas dan kebebasan kepada peserta didik dan guru dalam proses pembelajaran. Dengan adanya Projek P5, peserta didik dapat mengeksplorasi potensi diri mereka dan mengembangkan karakter Pancasila. Dengan adanya penyesuaian beban kerja dan penataan linieritas guru, guru dapat meningkatkan kualitas dan kesejahteraan mereka. Namun, Keputusan Menteri ini juga perlu diikuti dengan dukungan sarana dan prasarana, bantuan teknis, dan supervisi yang memadai dari pemerintah dan pihak terkait agar dapat dilaksanakan dengan efektif dan efisien.</p><div>Untuk dokumen lengkap dari <span style="text-align: justify;">Keputusan Menteri Pendidikan, Kebudayaan, Riset, dan Teknologi Republik Indonesia Nomor 262 tahun 2022 dapat dilihat berikut ini :</span></div><div><span style="text-align: justify;"><br /></span></div>
<iframe allow="autoplay" height="480" src="https://drive.google.com/file/d/14MGIr0qkdn2IpxfBpJiqbmE3FAMWJLpl/preview" width="640"></iframe>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0tag:blogger.com,1999:blog-7205043011098257996.post-84783200623002693652024-01-26T18:47:00.004+08:002024-01-26T20:02:36.056+08:00Panduan P5 dan PPRA untuk Madrasah<p><span style="text-align: justify;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGquImZGatYiA49XVbelgPdSxtkOGnhKLRcFfYJxOp_C1zxM2jN7MZO0gNnJKnwlxqB7o_JlpOj4Nz7ffxL_QxpexshfKwW8rGy3_YaDp9R5Na6kMvU5qay3MUiH-hZu4GSVqGYs2KPXtMfuFVs73NPsREiro1TxsnpnNOJCSAAw-NAJbCADJdsa-d7_0/s1755/3.%20Panduan%20P5%20PPRA_page-0001.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1755" data-original-width="1240" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGquImZGatYiA49XVbelgPdSxtkOGnhKLRcFfYJxOp_C1zxM2jN7MZO0gNnJKnwlxqB7o_JlpOj4Nz7ffxL_QxpexshfKwW8rGy3_YaDp9R5Na6kMvU5qay3MUiH-hZu4GSVqGYs2KPXtMfuFVs73NPsREiro1TxsnpnNOJCSAAw-NAJbCADJdsa-d7_0/w283-h400/3.%20Panduan%20P5%20PPRA_page-0001.jpg" width="283" /></a></span></div><span style="text-align: justify;"><br />Projek Penguatan Profil Pelajar
Pancasila dan Profil Pelajar Rahmatan Lil Alamin (P5 PPRA) adalah inisiatif
penting yang telah diluncurkan oleh Kementerian Agama Republik Indonesia pada
tahun 2022. Program ini dirancang untuk memberikan arah dan inspirasi bagi
madrasah di semua jenjang pendidikan, termasuk RA, MI, MTs, MA, dan MAK, dalam
mengembangkan kurikulum operasional mereka.</span><p></p><p><span style="text-align: justify;">Tujuan utama dari projek ini
adalah untuk memperkuat profil pelajar Pancasila dan profil pelajar Rahmatan
Lil Alamin dalam konteks madrasah. Ini mencakup prinsip-prinsip,
komponen-komponen, tahapan, kriteria output setiap tahapan perencanaan dan
pelaksanaan projek, strategi serta contoh-contoh pelaksanaan projek penguatan
Profil Pelajar Pancasila pada pembelajaran paradigma baru.</span></p><p><span style="text-align: justify;">Panduan ini diharapkan menjadi
salah satu sumber informasi yang dapat dirujuk oleh pendidik dalam merancang
dan melaksanakan projek. Meskipun panduan ini memberikan contoh strategi dan
format, pendidik diberi kebebasan untuk menggunakan rujukan, strategi, dan
format lain selama hasil yang diharapkan memenuhi kriteria output pada setiap
tahapan dan memenuhi prinsip pembelajaran dan asesmen yang telah ditetapkan.</span></p><p><span style="text-align: justify;">Dengan demikian, Projek Penguatan
Profil Pelajar Pancasila dan Profil Pelajar Rahmatan Lil Alamin merupakan upaya
penting untuk mencapai Profil Pelajar Pancasila dengan menggunakan Pembelajaran
Paradigma baru¹. Ini adalah langkah maju yang signifikan dalam pendidikan di
Indonesia, dan kami berharap ini akan membantu membentuk generasi baru pelajar
yang berdedikasi dan berpengetahuan.</span></p><p class="MsoNormal" style="text-align: justify;">Dalam panduan ini menjelaskan
tentang:</p><p class="MsoNormal" style="text-align: justify;"></p><ol><li>Memahami Projek Penguatan Profil
Pelajar Pancasila dan Profil Pelajar Rahmatan Lil Alamin</li><li>Menyiapkan Ekosistem Satuan
Pendidikan</li><li>Mendesain Projek Penguatan Profil
Pelajar Pancasila dan Profil Pelajar Rahmatan Lil Alamin</li><li>Mengolah Asesmen dan Melaporkan
Projek Penguatan Profil Pelajar Pancasila dan Profil Pelajar Rahmatan Lil
Alamin</li><li>Monitoring dan Evaluasi
Implementasi Projek Penguatan Profil Pelajar Pancasila dan Profil Pelajar
Rahmatan Lil Alamin</li></ol><p></p><p class="MsoNormal" style="text-align: justify;"><o:p></o:p></p><p class="MsoNormal" style="text-align: justify;"><o:p></o:p></p><p class="MsoNormal" style="text-align: justify;"><o:p></o:p></p><p class="MsoNormal" style="text-align: justify;"><o:p></o:p></p><p>
</p><p class="MsoNormal" style="text-align: justify;">Lebih lengkap tentang Projek
Penguatan Profil Pelajar Pancasila dan Profil Pelajar Rahmatan Lil Alamin dapat
dipelajari selengkapnya pada naskah berikut ini :</p><p class="MsoNormal" style="text-align: justify;"><o:p></o:p></p>
<iframe allow="autoplay" height="480" src="https://drive.google.com/file/d/1OXJUBICsLrKh5K8Jzspt17C27q2Szw32/preview" width="640"></iframe>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0tag:blogger.com,1999:blog-7205043011098257996.post-44818744340960809282023-10-13T08:43:00.006+08:002023-10-13T19:43:00.279+08:00Pembahasan Soal Sudut Pusat dan Sudut Keliling Lingkaran<p style="text-align: justify;"><span style="font-size: medium;">Sebelum membahas soal sudut pusat dan sudut keliling lingkaran, ada beberapa hal yang perlu diingat kembali yaitu.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Perhatikan lingkaran dengan pusat O dan berjari-jari r seperti pada gambar berikut.</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhemu0RnExNVSUAljf1Vez_U0vD1Bco2XlAIxZ57O_T3zJ_oK43ejrtixtJHXNQc1rXf-Hno6J3KHeKvhoD_RGjCboFPaFvzCpGqSayGqp914-UPwzWB-eL-ktIHRomKKjeI2mXHlVFzecTKWgRp8sblPmQmmL5fLAafUrQTGDkNeCdjnK2wb57pJxn568" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="" data-original-height="446" data-original-width="444" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEhemu0RnExNVSUAljf1Vez_U0vD1Bco2XlAIxZ57O_T3zJ_oK43ejrtixtJHXNQc1rXf-Hno6J3KHeKvhoD_RGjCboFPaFvzCpGqSayGqp914-UPwzWB-eL-ktIHRomKKjeI2mXHlVFzecTKWgRp8sblPmQmmL5fLAafUrQTGDkNeCdjnK2wb57pJxn568" width="239" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">Gambar 1. Hubungan sudur pusat, sudut keliling, panjang busur dan luas juring</span></td></tr></tbody></table></div><p></p><p style="text-align: justify;"></p><ul style="text-align: left;"><li><span style="font-size: medium;"><b style="text-align: justify;">Sudut Pusat</b><span style="text-align: justify;"> adalah sudut yang dibentuk oleh dua buah jari-jari dan titik sudutnya merupakan pusat lingkaran. Dari gambar diatas sudut pusatnya adalah </span><img src="https://latex.codecogs.com/svg.image?\angle&space;AOC=\alpha&space;" style="text-align: justify;" title="\angle AOC=\alpha" /></span></li><li style="text-align: justify;"><span style="font-size: medium;"><b>Sudut Keliling </b>adalah sudut yang dibentuk oleh dua buah tali busur yang berpotongan di satu titik dan titik sudutnya terletak pada keliling lingkaran. Dari gambar diatas sudut kelilingnya adalah <img src="https://latex.codecogs.com/svg.image?\angle&space;ABC=\beta&space;" style="text-align: left;" title="\angle ABC=\beta" /></span></li><li style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;AOC=2x\angle&space;ABC&space;" style="text-align: left;" title="\angle AOC=2x\angle ABC" /> jika kedua sudut tersebut menghadap busur yang sama</span></li><li style="text-align: justify;"><span style="font-size: medium;">Rumus panjang busur AC adalah <img src="https://latex.codecogs.com/svg.image?&space;AC=\frac{\alpha}{360^{\circ}}2\pi&space;r" style="text-align: left;" title="AC=\frac{\alpha}{360^{\circ}}2\pi r" /></span></li><li style="text-align: justify;"><span style="font-size: medium;">Rumus luas juring AOC adalah <img src="https://latex.codecogs.com/svg.image?L_{AOC}=\frac{\alpha}{360^{\circ}}\pi&space;r^{2}" style="text-align: left;" title="L_{AOC}=\frac{\alpha}{360^{\circ}}\pi r^{2}" /></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJSBl2S3D6DO1YlrP7j4TfNxBSrZKtta-Rg-3Gr6ftq75Ne_oeDRGREQQePDpzPG6__h3FkxNZT1xgTnb2cW0bjsq3zzOil3PlKdihblO-R25ZZPVsyXY4HlSRWt_cqV3nVbio1tjlrMKbSgorxOCRj9fbAr4M8WyvlApFKYdCqQ22Kt_D_9aYxcIJqus/s457/image-removebg-preview%20(4).png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img border="0" data-original-height="457" data-original-width="437" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJSBl2S3D6DO1YlrP7j4TfNxBSrZKtta-Rg-3Gr6ftq75Ne_oeDRGREQQePDpzPG6__h3FkxNZT1xgTnb2cW0bjsq3zzOil3PlKdihblO-R25ZZPVsyXY4HlSRWt_cqV3nVbio1tjlrMKbSgorxOCRj9fbAr4M8WyvlApFKYdCqQ22Kt_D_9aYxcIJqus/s320/image-removebg-preview%20(4).png" width="306" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">Gambar 2. Hubungan besar sudut keliling</span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><ul style="text-align: left;"><li><span style="font-size: medium;">Besar sudut-sudut keliling yang menghadap busur yang sama adalah sama besar. <img src="https://latex.codecogs.com/svg.image?\angle&space;ABC=\angle&space;ADC=\angle&space;AEC=\beta&space;" title="\angle ABC=\angle ADC=\angle AEC=\beta" /></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH9uTgF5ipEMvrQPN-fpDpBIZrSVcR7FdXNH8nlKs9QIBt1zXDxSWMWiA7ail3jFq7pyBeZZsUaTsR4ybi9JOLW1utWb0RNZdH17mfzK3mNWj07XBanFfeZS5QlFcMI87fFawcznlqz_OU_PxEfnInSORhuBNhILesgXRgHtONbtclmEc079yJerDIaCE/s485/image-removebg-preview%20(5).png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img border="0" data-original-height="485" data-original-width="444" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH9uTgF5ipEMvrQPN-fpDpBIZrSVcR7FdXNH8nlKs9QIBt1zXDxSWMWiA7ail3jFq7pyBeZZsUaTsR4ybi9JOLW1utWb0RNZdH17mfzK3mNWj07XBanFfeZS5QlFcMI87fFawcznlqz_OU_PxEfnInSORhuBNhILesgXRgHtONbtclmEc079yJerDIaCE/s320/image-removebg-preview%20(5).png" width="293" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">Gambar 3. Hubungan sudut keliling yang saling berhadapan</span></td></tr></tbody></table><span style="font-size: medium;"><br /></span><div><ul style="text-align: left;"><li><span style="font-size: medium;">Jumlah sudut dari sudut kelililing yang saling berhadapan adalah <img src="https://latex.codecogs.com/svg.image?180^{o}" title="180^{o}" />. <img src="https://latex.codecogs.com/svg.image?\angle&space;ABC+\angle&space;CFA=180^{o}" title="\angle ABC+\angle CFA=180^{o}" /></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2nrlNP7MrPcbMVznqEwAFc88BnfO28ghchBRmVxf7Je52QmZRGztyb5WQuj-ldcuEGTeJ2GrcUroVwvMe3QcnEHO-KHHQECjSowqwasw6IeVxKZcRj0bvH_tKgxr_qX_hmlHdcmTZ5xOcnQPgOZo2w-hJ6C6Yii0vGJiFqPvBduDkT4tjGZSmmkzzBus/s446/image-removebg-preview%20(6).png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img border="0" data-original-height="400" data-original-width="446" height="287" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2nrlNP7MrPcbMVznqEwAFc88BnfO28ghchBRmVxf7Je52QmZRGztyb5WQuj-ldcuEGTeJ2GrcUroVwvMe3QcnEHO-KHHQECjSowqwasw6IeVxKZcRj0bvH_tKgxr_qX_hmlHdcmTZ5xOcnQPgOZo2w-hJ6C6Yii0vGJiFqPvBduDkT4tjGZSmmkzzBus/s320/image-removebg-preview%20(6).png" width="320" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">Gambar 4. Sudut keliling menghadap diameter lingkaran</span></td></tr></tbody></table><span style="font-size: medium;"><br /></span><div><ul style="text-align: left;"><li><span style="font-size: medium;">Sudut keliling yang meghadap diameter lingkaran membentuk sudut siku-siku</span></li></ul><div><span style="font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><b>Pembahasan Soal Sudut Pusat dan Sudut Keliling Lingkaran</b></span></div><div><p><span style="font-size: medium;">1. Perhatikan gambar berikut !</span></p><p></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgSzU-lJ7ugViSRi9nh0de3wuFGP3aRcgzLCMkv8q9fhrOP790MJhYfv15YJLYg1RanRhUx6yxpsMBol5_Po1l7ydib-WHjklCmuF2HpE4YsonZsVaebT6-NbymA0oNlkYJIqkFmbsSdhn7rvuysOw6fEFDGKKwmW6KpktVLyH-s7BMAZFN70XZPuEe" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="227" data-original-width="272" height="191" src="https://blogger.googleusercontent.com/img/a/AVvXsEgSzU-lJ7ugViSRi9nh0de3wuFGP3aRcgzLCMkv8q9fhrOP790MJhYfv15YJLYg1RanRhUx6yxpsMBol5_Po1l7ydib-WHjklCmuF2HpE4YsonZsVaebT6-NbymA0oNlkYJIqkFmbsSdhn7rvuysOw6fEFDGKKwmW6KpktVLyH-s7BMAZFN70XZPuEe=w229-h191" title="Pembahasan Soal Semester Genap Kelas 8" width="229" /></span></a></p><p></p><p><span style="font-size: medium;">Jika <img src="https://latex.codecogs.com/svg.image?\angle&space;BOC=70^{o}" title="https://latex.codecogs.com/svg.image?\angle BOC=70^{o}" />, maka besar <img src="https://latex.codecogs.com/svg.image?\angle&space;OAB" title="https://latex.codecogs.com/svg.image?\angle OAB" /> adalah ....</span></p><p><span style="font-size: medium;">A. <img src="https://latex.codecogs.com/svg.image?25^{o}" title="https://latex.codecogs.com/svg.image?25^{o}" /></span></p><p><span style="font-size: medium;">B. <img src="https://latex.codecogs.com/svg.image?30^{o}" title="https://latex.codecogs.com/svg.image?30^{o}" /></span></p><p><span style="font-size: medium;">C. <img src="https://latex.codecogs.com/svg.image?35^{o}" title="https://latex.codecogs.com/svg.image?35^{o}" /></span></p><p><span style="font-size: medium;">D. <img src="https://latex.codecogs.com/svg.image?45^{o}" title="https://latex.codecogs.com/svg.image?45^{o}" /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><b>Pembahasan</b></span></p><p></p><blockquote><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOC&space;" style="text-align: justify;" /><span style="text-align: justify;"> merupakan sudut pusat dan </span><img src="https://latex.codecogs.com/svg.image?\angle&space;OAB" style="text-align: justify;" /><span style="text-align: justify;"> merupakan sudut keliling. Hubungan antara sudut pusat dan sudut keliling yang menghadap busur yang sama adalah</span></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\mathrm{Sudut\,&space;\,&space;Keliling}=\frac{1}{2}\mathrm{Sudut\,&space;\,&space;Pusat}" style="text-align: justify;" /></span></p><p></p></blockquote><p><span style="font-size: medium; text-align: justify;"><br /></span></p><p><span style="font-size: medium; text-align: justify;">Sehingga diperoleh</span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;OAB=\frac{1}{2}\angle&space;BOC&space;" title="https://latex.codecogs.com/svg.image?\angle OAB=\frac{1}{2}\angle BOC" /></span></p><p><span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{1}{2}.70^{o}&space;" title="https://latex.codecogs.com/svg.image?=\frac{1}{2}.70^{o}" /></span></p><p><span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=35^{o}" title="https://latex.codecogs.com/svg.image?=35^{o}" /></span></p></div><div><p><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C </b></span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="\blacksquare" /></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">2. Perhatikan gambar berikut</span></p><p></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjcl4CdTMDQW8Qqo_ZbqOARPWq7geP69b0foc3hEZMBfSWqvZpXOUn_hwFKu5YO1NmECWkRxGEIIwtjFfK_LnqRUQ_7_KCUegmeq9Ky9KliJfLanI1E8SgkdhFoq7HpEIc9OMKRMTirU8iCZ3pEN7TsJJX_vWj34CE97Oz-Spc5tvr3ZhQFeHu_ARyi" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="207" data-original-width="230" height="164" src="https://blogger.googleusercontent.com/img/a/AVvXsEjcl4CdTMDQW8Qqo_ZbqOARPWq7geP69b0foc3hEZMBfSWqvZpXOUn_hwFKu5YO1NmECWkRxGEIIwtjFfK_LnqRUQ_7_KCUegmeq9Ky9KliJfLanI1E8SgkdhFoq7HpEIc9OMKRMTirU8iCZ3pEN7TsJJX_vWj34CE97Oz-Spc5tvr3ZhQFeHu_ARyi=w182-h164" title="Pembahasan Soal Semester Genap Kelas 8" width="182" /></span></a></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Titik O adalah pusat lingkaran. Jika diketahui <img src="https://latex.codecogs.com/svg.image?\angle&space;ABE+\angle&space;ACE+\angle&space;ADE=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ABE+\angle ACE+\angle ADE=96^{o}" />, maka besar <img src="https://latex.codecogs.com/svg.image?\angle&space;AOE" title="https://latex.codecogs.com/svg.image?\angle AOE" /> adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. <img src="https://latex.codecogs.com/svg.image?32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?48^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?48^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?54^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?54^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?64^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?64^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ingat bahwa besarnya sudut keliling yang menghadap busur yang sama memiliki besar sama.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil <img src="https://latex.codecogs.com/svg.image?\angle&space;ACE" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ACE" /> dan misal <img src="https://latex.codecogs.com/svg.image?\angle&space;ACE=x" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ACE=x" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena <img src="https://latex.codecogs.com/svg.image?\angle&space;ABE=\angle&space;ACE=\angle&space;ADE" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ABE=\angle ACE=\angle ADE" />, maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;ABE+\angle&space;ACE+\angle&space;ADE=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ABE+\angle ACE+\angle ADE=96^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?x+x+x=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x+x+x=96^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?3x=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?3x=96^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?x=\frac{96^{o}}{3}=32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x=\frac{96^{o}}{3}=32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?\angle&space;AOE=2\angle&space;ACE&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle AOE=2\angle ACE" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=2.32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=2.32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=64^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=64^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : D </b></span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="\blacksquare" /></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">3. Nilai <i>x</i> dari gambar dibawah adalah ....</span></p><p style="text-align: justify;"></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEixEzMWR_Gm0Um8aI74j-GZZCu8j31D6b-5nUnbCZaVX5U2q9r7f8xB8-vfsxAY5tKTkKF_ccpPZPuPnf4TeG0vSkhUe38Bby1El0qBqpKrckgyPhHkZlwlzXjFdrjI6bcttnGoaWWLNaCQk0vKLPWgynnJ-bIl0MFsJV-oQGKZr-drSbaWoASZp1kX" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="235" data-original-width="235" height="167" src="https://blogger.googleusercontent.com/img/a/AVvXsEixEzMWR_Gm0Um8aI74j-GZZCu8j31D6b-5nUnbCZaVX5U2q9r7f8xB8-vfsxAY5tKTkKF_ccpPZPuPnf4TeG0vSkhUe38Bby1El0qBqpKrckgyPhHkZlwlzXjFdrjI6bcttnGoaWWLNaCQk0vKLPWgynnJ-bIl0MFsJV-oQGKZr-drSbaWoASZp1kX=w167-h167" title="Pembahasan Soal Semester Genap Kelas 8" width="167" /></span></a></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">A. <img src="https://latex.codecogs.com/svg.image?32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?36^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?36^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?42^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?42^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?46^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?46^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ingat bahwa sudut keliling yang saling berhadapan dan kaki-kaki sudutnya berimpit memiliki jumlah besar sudut <img src="https://latex.codecogs.com/svg.image?180^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BAD+\angle&space;BCD=180^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle BAD+\angle BCD=180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?2x+3x=180^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?2x+3x=180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?5x=180^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?5x=180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?x=36^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x=36^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : B </b></span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="\blacksquare" /></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Perhatikan gambar berikut</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-T8NIjynQAbKjNjQD0ifa0IOPD0SfF_rx7bic1nKO6UywIfwIcGJg1OuOznVaqbrunf58FeSCffsUNDkM5svgf27js6lXcltOqO5DOMh04yZ4PEWI5BEYvQh9i6pqsGImnj2GTsS725IMTkXc-MWh0n-OpjYSWlj0tX2aciDTdCoQ_3rK4euWILKEAtA/s350/image-removebg-preview%20(7).png" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img border="0" data-original-height="333" data-original-width="350" height="304" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-T8NIjynQAbKjNjQD0ifa0IOPD0SfF_rx7bic1nKO6UywIfwIcGJg1OuOznVaqbrunf58FeSCffsUNDkM5svgf27js6lXcltOqO5DOMh04yZ4PEWI5BEYvQh9i6pqsGImnj2GTsS725IMTkXc-MWh0n-OpjYSWlj0tX2aciDTdCoQ_3rK4euWILKEAtA/s320/image-removebg-preview%20(7).png" width="320" /></span></a></div><span style="font-size: medium;">Tentukan besar <img src="https://latex.codecogs.com/svg.image?\angle&space;BDE" title="\angle BDE" />, <img src="https://latex.codecogs.com/svg.image?\angle&space;BCE" title="\angle BCE" />, dan <img src="https://latex.codecogs.com/svg.image?\angle&space;CBE" title="\angle CBE" /></span></div></div></div><div><span style="font-size: medium;"><br /></span></div><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOC+\angle&space;BOE=180^{o}" title="\angle BOC+\angle BOE=180^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?&space;105^{o}+\angle&space;BOE=180^{o}" title="105^{o}+\angle BOE=180^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOE=180^{o}-105^{o}" title="\angle BOE=180^{o}-105^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOE=75^{o}" title="\angle BOE=75^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan bahwa <img src="https://latex.codecogs.com/svg.image?\angle&space;BDE" title="\angle BDE" /> dan <img src="https://latex.codecogs.com/svg.image?\angle&space;BOE" title="\angle BOE" /> menghadap busur yang sama yaitu busur BE, maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BDE=\frac{1}{2}\angle&space;BOE" title="\angle BDE=\frac{1}{2}\angle BOE" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{1}{2}75^{o}" title="=\frac{1}{2}75^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=37,5^{o}" title="=37,5^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan bahwa <img src="https://latex.codecogs.com/svg.image?\angle&space;BDE" title="\angle BDE" /> menghadap busur yang sama dengan <img src="https://latex.codecogs.com/svg.image?\angle&space;BCE" title="\angle BCE" /> yaitu busur BE, maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BDE=\angle&space;BCE" title="\angle BDE=\angle BCE" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=37,5^{o}" title="=37,5^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan gambar dibawah</span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie7YU-NJRB7ywu9Czl8GokKLqwJvVE8Y4kj5V6YJefhsYxU7hd8dJi60AHqyFZ_x_2b1hVfSsL63fNr_FFB_WEi8LuXd5glohbcVycxsXe5X4mVpKoyluZhy-kH0yudl2d0pnrftN71OTKl8OGy-etOcjWunee4sRTVXpxPnq2VJQC2LKhYZWjDygtWWA/s334/image-removebg-preview%20(8).png" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img border="0" data-original-height="324" data-original-width="334" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie7YU-NJRB7ywu9Czl8GokKLqwJvVE8Y4kj5V6YJefhsYxU7hd8dJi60AHqyFZ_x_2b1hVfSsL63fNr_FFB_WEi8LuXd5glohbcVycxsXe5X4mVpKoyluZhy-kH0yudl2d0pnrftN71OTKl8OGy-etOcjWunee4sRTVXpxPnq2VJQC2LKhYZWjDygtWWA/s320/image-removebg-preview%20(8).png" width="320" /></span></a></div><p style="text-align: left;"><span style="font-size: medium;">Dari gambar terlihat bahwa <img src="https://latex.codecogs.com/svg.image?\angle&space;CBE" title="\angle CBE" /> menghadap diameter lingkaran maka <img src="https://latex.codecogs.com/svg.image?\angle&space;CBE=90^{o}" title="\angle CBE=90^{o}" /> </span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" title="\blacksquare" /></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">5. Perhatikan gambar berikut</span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheOcH7Vht8AztP-rTLVg5XM32foMNBlGkp3MdRLCqTHaO4MWwVoElx9f_T06u3xNt692pJmmMtpxHu9A4CaJZzEosetqgB2ZO3pbfmJFJhyGfznflhWePaTdG7NEpwh7JlktMy6Ik1V3QV9UEfsIOgEo3lJTUnvbO_0BX639Dtr5Pr54iCcELhb0z3ceQ/s466/image-removebg-preview%20(9).png" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img border="0" data-original-height="452" data-original-width="466" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheOcH7Vht8AztP-rTLVg5XM32foMNBlGkp3MdRLCqTHaO4MWwVoElx9f_T06u3xNt692pJmmMtpxHu9A4CaJZzEosetqgB2ZO3pbfmJFJhyGfznflhWePaTdG7NEpwh7JlktMy6Ik1V3QV9UEfsIOgEo3lJTUnvbO_0BX639Dtr5Pr54iCcELhb0z3ceQ/s320/image-removebg-preview%20(9).png" width="320" /></span></a></div><p style="text-align: left;"><span style="font-size: medium;">Jika QN adalah tangen dari lingkaran, tentukan besar <img src="https://latex.codecogs.com/svg.image?\angle&space;OQN" title="\angle OQN" />.</span></p><p style="text-align: left;"><b><span style="font-size: medium;">Pembahasan</span></b></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan <img src="https://latex.codecogs.com/svg.image?\angle&space;QON" title="\angle QON" /> (sudut pusat lingkaran) dan <img src="https://latex.codecogs.com/svg.image?\angle&space;PMN" title="\angle PMN" /> (sudut keliling lingkaran) menghadap busur yang sama yaitu busu PN, maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;QON=2\angle&space;PMN=2.25^{o}=50^{o}" title="\angle QON=2\angle PMN=2.25^{o}=50^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan segitiga ONQ</span></p><p style="text-align: left;"><span style="font-size: medium;">Diketahui <img src="https://latex.codecogs.com/svg.image?\angle&space;ONQ=90^{o}" title="\angle ONQ=90^{o}" /> maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;ONQ+\angle&space;QON+\angle&space;OQN=180^{o}" title="\angle ONQ+\angle QON+\angle OQN=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?90^{o}+50^{o}+\angle&space;OQN=180^{o}" title="90^{o}+50^{o}+\angle OQN=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span><img src="https://latex.codecogs.com/svg.image?\angle&space;OQN=180^{o}-140^{o}=40^{o}" title="\angle OQN=180^{o}-140^{o}=40^{o}" /><span> </span></span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" title="\blacksquare" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">6. Perhatikan gambar berikut</span></p><p style="text-align: left;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Jl_k1cHzX-BGO0zKDYzpcNfcro3rw_mHnCZuDVTz7X9CGGsKg1sRPogFpvsP_JRQceWSJCwFN-hl-mp3c3FY5mHBDDt4MCJwd8B4Q1L-AXIlgoy_v08hbYBqo2MaREcOXQ7bN7AZFIY5On8OWbJUVADm0pElCtvi2VSkGJ1DoXBmYAgpXUHA-qJMgxA/s445/image-removebg-preview%20(10).png" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img border="0" data-original-height="412" data-original-width="445" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Jl_k1cHzX-BGO0zKDYzpcNfcro3rw_mHnCZuDVTz7X9CGGsKg1sRPogFpvsP_JRQceWSJCwFN-hl-mp3c3FY5mHBDDt4MCJwd8B4Q1L-AXIlgoy_v08hbYBqo2MaREcOXQ7bN7AZFIY5On8OWbJUVADm0pElCtvi2VSkGJ1DoXBmYAgpXUHA-qJMgxA/s320/image-removebg-preview%20(10).png" width="320" /></span></a></div><p style="text-align: left;"><span style="font-size: medium;">Dari gambar diatas, tentukan besar <img src="https://latex.codecogs.com/svg.image?\angle&space;ODC" title="\angle ODC" />.</span></p><p style="text-align: left;"><b><span style="font-size: medium;">Pembahasan</span></b></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan bahwa <img src="https://latex.codecogs.com/svg.image?\angle&space;BAD" title="\angle BAD" /> menghadap busur yang sama dengan <img src="https://latex.codecogs.com/svg.image?\angle&space;BOD" title="\angle BOD" />, maka diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOD=2.\angle&space;BAD" title="\angle BOD=2.\angle BAD" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=2.75^{o}" title="=2.75^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=150^{o}" title="=150^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan bahwa <img src="https://latex.codecogs.com/svg.image?\angle&space;ODB=\angle&space;OBD" title="\angle ODB=\angle OBD" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">(Mengapa demikian? perhatikan bahwa segitiga BOD membentuk segitiga sama kaki. Berdasarkan sifat dari segitiga sama kaki, maka besar sudut kaki-kakinya sama besar)</span></p><p style="text-align: left;"><span style="font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOD+\angle&space;ODB+\angle&space;OBD=180^{o}" title="\angle BOD+\angle ODB+\angle OBD=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOD+2\angle&space;ODB=180^{o}" title="\angle BOD+2\angle ODB=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?150^{o}+2\angle&space;ODB=180^{o}" title="150^{o}+2\angle ODB=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?2\angle&space;ODB=180^{o}-150^{o}" title="2\angle ODB=180^{o}-150^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?2\angle&space;ODB=30^{o}" title="2\angle ODB=30^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;ODB=15^{o}" title="\angle ODB=15^{o}" /> .............(1)</span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan bahwa <img src="https://latex.codecogs.com/svg.image?\angle&space;BAD" title="\angle BAD" /> dan <img src="https://latex.codecogs.com/svg.image?\angle&space;BCD" title="\angle BCD" /> adalah sudut keliling yang saling berhadapan, sehingga diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BAD+\angle&space;BCD=180^{o}" title="\angle BAD+\angle BCD=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?75^{o}+\angle&space;BCD=180^{o}" title="75^{o}+\angle BCD=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BCD=180^{o}-75^{o}" title="\angle BCD=180^{o}-75^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BCD=105^{o}" title="\angle BCD=105^{o}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan juga bahwa</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BCD+\angle&space;CBD+\angle&space;BDC=180^{o}" title="\angle BCD+\angle CBD+\angle BDC=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?105^{o}+27^{o}+\angle&space;BDC=180^{o}" title="105^{o}+27^{o}+\angle BDC=180^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BDC=180^{o}-132^{o}" title="\angle BDC=180^{o}-132^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BDC=48^{o}" title="\angle BDC=48^{o}" /> .........(2)</span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan sudut <img src="https://latex.codecogs.com/svg.image?\angle&space;ODC" title="\angle ODC" /> dan persamaan (1) dan (2) diatas, diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;ODC=\angle&space;BDC+\angle&space;ODB" title="\angle ODC=\angle BDC+\angle ODB" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;ODC=48^{o}+15^{o}" title="\angle ODC=48^{o}+15^{o}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;ODC=63^{o}" title="\angle ODC=63^{o}" /><span> </span> <img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" title="\blacksquare" /></span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0tag:blogger.com,1999:blog-7205043011098257996.post-44982232104579580002023-10-11T19:12:00.008+08:002023-10-11T20:02:49.713+08:00Pembahasan Soal Persamaan Eksponen<p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjxQJHwHwQgTQy3VOvu5kIC08R5pNglRoJQmRc-b8Tz-g23qOkPwmflZq_rB3c4x4Uc6ytM1T7Wjo4r9VeAzQD43S6tTPwtc_QN1GtC2msudvE_v0zhaicj5Pb5SKGyuHCtAI-Ddh0Lle3mUdos_AfJpkpkZn-LFkWuCr8JanQ4jwpm1thrmBn_IQIjzg/s195/cooltext389393513213664.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="195" data-original-width="195" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjxQJHwHwQgTQy3VOvu5kIC08R5pNglRoJQmRc-b8Tz-g23qOkPwmflZq_rB3c4x4Uc6ytM1T7Wjo4r9VeAzQD43S6tTPwtc_QN1GtC2msudvE_v0zhaicj5Pb5SKGyuHCtAI-Ddh0Lle3mUdos_AfJpkpkZn-LFkWuCr8JanQ4jwpm1thrmBn_IQIjzg/w111-h111/cooltext389393513213664.png" style="float: left; margin: 5px 9px;" width="111" /></a></div><div style="text-align: justify;">Persamaan Eksponen merupakan salah satu materi pokok pada mata pelajaran Matematika kelas 10 kurikulum merdeka, berikut kami berikan beberapa soal pembahasan soal persamaan eksponen. Pembahasan soal ini untuk menjawab pertanyaan yang ditanyakan di group Matematika Indonesia, semoga pembahasan soal persamaan eksponen ini dapat membantu untuk lebih memahami penyelesaian dari persamaan eksponen. Selamat Belajar.........</div><p></p><p>Tentukan nilai x dari persamaan berikut.</p><p>1. <img src="https://latex.codecogs.com/svg.image?&space;7^{x}=49" title="7^{x}=49" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?&space;7^{x}=49" title="7^{x}=49" /></p><p><img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;7^{x}=7^{2}" title="\Leftrightarrow 7^{x}=7^{2}" /> (Bilangan pokok sudah sama)</p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=2" title="\Rightarrow x=2" /></p><p><br /></p><p>2. <img src="https://latex.codecogs.com/svg.image?5^{x}=625" title="5^{x}=625" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?5^{x}=625" title="5^{x}=625" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;5^{x}=5^{4}" title="\Leftrightarrow 5^{x}=5^{4}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=4" title="\Rightarrow x=4" /></p><p><br /></p><p>3. <img src="https://latex.codecogs.com/svg.image?2^{x}=8" title="2^{x}=8" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?2^{x}=8" title="2^{x}=8" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{x}=2^{3}" title="\Leftrightarrow 2^{x}=2^{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=3" title="\Rightarrow x=3" /></p><p><br /></p><p>4. <img src="https://latex.codecogs.com/svg.image?3^{-x}=81" title="3^{-x}=81" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?3^{-x}=81" title="3^{-x}=81" /></p><p><img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;3^{-x}=3^{4}" title="\Leftrightarrow 3^{-x}=3^{4}" /></p><p><img src="https://latex.codecogs.com/svg.image?\Rightarrow-x=4" title="\Rightarrow-x=4" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=-4" title="\Rightarrow x=-4" /></p><p><br /></p><p>5. <img src="https://latex.codecogs.com/svg.image?2^{3x}=256" title="2^{3x}=256" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?2^{3x}=256" title="2^{3x}=256" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{3x}=2^{8}" title="\Leftrightarrow 2^{3x}=2^{8}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;3x=8" title="\Rightarrow 3x=8" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{8}{3}" title="\Rightarrow x=\frac{8}{3}" /></p><p><br /></p><p>6. <img src="https://latex.codecogs.com/svg.image?25^{x}=125" title="25^{x}=125" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?25^{x}=125" title="25^{x}=125" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(5^{2}\right)^{x}=5^{3}" title="\Leftrightarrow\left(5^{2}\right)^{x}=5^{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;5^{2x}=5^{3}" title="\Leftrightarrow 5^{2x}=5^{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x=3" title="\Rightarrow 2x=3" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{3}{2}" title="\Rightarrow x=\frac{3}{2}" /></p><p><br /></p><p>7. <img src="https://latex.codecogs.com/svg.image?8^{x}=\sqrt{2}" title="8^{x}=\sqrt{2}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?8^{x}=\sqrt{2}" title="8^{x}=\sqrt{2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(2^{3}\right)^{x}=2^{\frac{1}{2}}" title="\Leftrightarrow\left(2^{3}\right)^{x}=2^{\frac{1}{2}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{3x}=2^{\frac{1}{2}}" title="\Leftrightarrow 2^{3x}=2^{\frac{1}{2}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;3x=\frac{1}{2}" title="\Rightarrow 3x=\frac{1}{2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{\frac{1}{2}}{3}" title="\Rightarrow x=\frac{\frac{1}{2}}{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{1}{2}.\frac{1}{3}" title="\Rightarrow x=\frac{1}{2}.\frac{1}{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{1}{6}" title="\Rightarrow x=\frac{1}{6}" /></p><p><br /></p><p>8. <img src="https://latex.codecogs.com/svg.image?9^{2x-1}=2187" title="9^{2x-1}=2187" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?9^{2x-1}=2187" title="9^{2x-1}=2187" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(3^{2}\right)^{2x-1}=3^{7}" title="\Leftrightarrow\left(3^{2}\right)^{2x-1}=3^{7}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;3^{4x-2}=3^{7}" title="\Leftrightarrow 3^{4x-2}=3^{7}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;4x-2=7" title="\Rightarrow 4x-2=7" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;4x=7+2" title="\Rightarrow 4x=7+2" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;4x=9" title="\Rightarrow 4x=9" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{9}{4}" title="\Rightarrow x=\frac{9}{4}" /></p><p><br /></p><p>9. <img src="https://latex.codecogs.com/svg.image?0,0001^{x}=0,1" title="0,0001^{x}=0,1" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?0,0001^{x}=0,1" title="0,0001^{x}=0,1" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(10^{-4}\right)^{x}=10^{-1}" title="\Leftrightarrow\left(10^{-4}\right)^{x}=10^{-1}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;10^{-4x}=10^{-1}" title="\Leftrightarrow 10^{-4x}=10^{-1}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow-4x=-1" title="\Rightarrow-4x=-1" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{-1}{-4}" title="\Rightarrow x=\frac{-1}{-4}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{1}{4}" title="\Rightarrow x=\frac{1}{4}" /></p><p><br /></p><p>10. <img src="https://latex.codecogs.com/svg.image?\left(-4\right)^{x}=\frac{1}{16}" title="\left(-4\right)^{x}=\frac{1}{16}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?\left(-4\right)^{x}=\frac{1}{16}" title="\left(-4\right)^{x}=\frac{1}{16}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(-4\right)^{x}=\frac{1}{4^{2}}" title="\Leftrightarrow\left(-4\right)^{x}=\frac{1}{4^{2}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(-4\right)^{x}={4^{-2}" title="\Leftrightarrow\left(-4\right)^{x}={4^{-2}" /></p><p>Karena bilangan pokok tidak sama maka tidak ada nilai x yang memenuhi persamaan eksponensial tersebut.</p><p><br /></p><p>11. <img src="https://latex.codecogs.com/svg.image?3^{2x-1}=\frac{1}{27}" title="3^{2x-1}=\frac{1}{27}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?3^{2x-1}=\frac{1}{27}" title="3^{2x-1}=\frac{1}{27}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;3^{2x-1}=\frac{1}{3^{3}}" title="\Leftrightarrow 3^{2x-1}=\frac{1}{3^{3}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;3^{2x-1}=3^{-3}" title="\Leftrightarrow 3^{2x-1}=3^{-3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x-1=-3" title="\Rightarrow 2x-1=-3" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x=-3+1" title="\Rightarrow 2x=-3+1" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x=-2" title="\Rightarrow 2x=-2" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{-2}{2}" title="\Rightarrow x=\frac{-2}{2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=-1" title="\Rightarrow x=-1" /></p><p><br /></p><p>12. <img src="https://latex.codecogs.com/svg.image?4^{2x-1}=8" title="4^{2x-1}=8" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?4^{2x-1}=8" title="4^{2x-1}=8" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(2^{2}\right)^{2x-1}=2^{3}" title="\Leftrightarrow\left(2^{2}\right)^{2x-1}=2^{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{4x-2}=2^{3}" title="\Leftrightarrow 2^{4x-2}=2^{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;4x-2=3" title="\Rightarrow 4x-2=3" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;4x=3+2" title="\Rightarrow 4x=3+2" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;4x=5" title="\Rightarrow 4x=5" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{5}{4}" title="\Rightarrow x=\frac{5}{4}" /></p><p><br /></p><p>13. <img src="https://latex.codecogs.com/svg.image?5^{x-9}=25^{3-x}" title="5^{x-9}=25^{3-x}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?5^{x-9}=25^{3-x}" title="5^{x-9}=25^{3-x}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;5^{x-9}=\left(5^{2}\right)^{3-x}" title="\Leftrightarrow 5^{x-9}=\left(5^{2}\right)^{3-x}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;5^{x-9}=5^{6-2x}" title="\Leftrightarrow 5^{x-9}=5^{6-2x}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x-9=6-2x" title="\Rightarrow x-9=6-2x" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x+2x=6+9" title="\Rightarrow x+2x=6+9" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;3x=15" title="\Rightarrow 3x=15" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{15}{3}" title="\Rightarrow x=\frac{15}{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=5" title="\Rightarrow x=5" /></p><p><br /></p><p>14. <img src="https://latex.codecogs.com/svg.image?\sqrt{5^{x+2}}=25^{x-2}" title="\sqrt{5^{x+2}}=25^{x-2}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?\sqrt{5^{x+2}}=25^{x-2}" title="\sqrt{5^{x+2}}=25^{x-2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(5^{x+2}\right)^{\frac{1}{2}}=\left(5^{2}\right)^{x-2}" title="\Leftrightarrow\left(5^{x+2}\right)^{\frac{1}{2}}=\left(5^{2}\right)^{x-2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;5^{\frac{1}{2}x+1}=5^{2x-4}" title="\Leftrightarrow 5^{\frac{1}{2}x+1}=5^{2x-4}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow\frac{1}{2}x+1=2x-4" title="\Rightarrow\frac{1}{2}x+1=2x-4" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow\frac{1}{2}x-2x=-4-1" title="\Rightarrow\frac{1}{2}x-2x=-4-1" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow-\frac{3}{2}x=-5" title="\Rightarrow-\frac{3}{2}x=-5" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{10}{3}" title="\Rightarrow x=\frac{10}{3}" /></p><p><br /></p><p>15. <img src="https://latex.codecogs.com/svg.image?3^{x^{2}+3x}=3^{x+8}" title="3^{x^{2}+3x}=3^{x+8}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?3^{x^{2}+3x}=3^{x+8}" title="3^{x^{2}+3x}=3^{x+8}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x^{2}+3x=x+8" title="\Rightarrow x^{2}+3x=x+8" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x^{2}+3x-x-8=0" title="\Rightarrow x^{2}+3x-x-8=0" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x^{2}+2x-8=0" title="\Rightarrow x^{2}+2x-8=0" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow\left(x+4\right)\left(x-2\right)=0" title="\Rightarrow\left(x+4\right)\left(x-2\right)=0" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow\left(x+4\right)=0\:\textrm{atau}\left(x-2\right)=0" title="\Rightarrow\left(x+4\right)=0\:\textrm{atau}\left(x-2\right)=0" /></p><p>
<span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?x=-4" title="x=-4" />
<span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?x=2" title="x=2" /></p><p>Jadi nilai x yang memenuhi adalah x = -4 atau x = 2</p><p><br /></p><p>16. <img src="https://latex.codecogs.com/svg.image?25^{x^{2}-3x+7}=125^{x-2}" title="25^{x^{2}-3x+7}=125^{x-2}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?25^{x^{2}-3x+7}=125^{x-2}" title="25^{x^{2}-3x+7}=125^{x-2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(5^{2}\right)^{x^{2}-3x+7}=\left(5^{3}\right)^{x-2}" title="\Leftrightarrow\left(5^{2}\right)^{x^{2}-3x+7}=\left(5^{3}\right)^{x-2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;5^{2x^{2}-6x+14}=5^{3x-6}" title="\Leftrightarrow 5^{2x^{2}-6x+14}=5^{3x-6}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x^{2}-6x+14=3x-6" title="\Rightarrow 2x^{2}-6x+14=3x-6" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x^{2}-6x-3x+14+6=0" title="\Rightarrow 2x^{2}-6x-3x+14+6=0" /></p><p><img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x^{2}-9x+20=0" title="\Rightarrow 2x^{2}-9x+20=0" /></p><p>Kita akan cek nilai diskriminan dari persamaan kuadrat diatas</p><p>
<img src="https://latex.codecogs.com/svg.image?D=b^{2}-4ac" title="D=b^{2}-4ac" /></p><p>
<span> </span><img src="https://latex.codecogs.com/svg.image?=(-9)^{2}-4.2.20" title="=(-9)^{2}-4.2.20" /></p><p>
<span> </span><img src="https://latex.codecogs.com/svg.image?=81-160" title="=81-160" /></p><p>
<span> </span><img src="https://latex.codecogs.com/svg.image?=-79" title="=-79" /></p><p>Karena nilai D < 0 atau diskriminan bernilai negatif maka tidak ada nilai x bilangan real yang memenuhi persamaan eksponen tersebut.</p><p>Untuk mengingat kembali nilai diskriminan ini silahkan pelajari kembali disini <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/menentukan-akar-persamaan-kuadrat.html" target="_blank">https://matematikasmpmts.sambimatika.my.id/2021/08/menentukan-akar-persamaan-kuadrat.html</a></p><p><br /></p><p>17. <img src="https://latex.codecogs.com/svg.image?&space;2^{x^{2}+x}=4^{x+1}" title="2^{x^{2}+x}=4^{x+1}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?&space;2^{x^{2}+x}=4^{x+1}" title="2^{x^{2}+x}=4^{x+1}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{x^{2}+x}=\left(2^{2}\right)^{x+1}" title="\Leftrightarrow 2^{x^{2}+x}=\left(2^{2}\right)^{x+1}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{x^{2}+x}=2^{2x+2}" title="\Leftrightarrow 2^{x^{2}+x}=2^{2x+2}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x^{2}+x=2x+2" title="\Rightarrow x^{2}+x=2x+2" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x^{2}+x-2x-2=0" title="\Rightarrow x^{2}+x-2x-2=0" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x^{2}-x-2=0" title="\Rightarrow x^{2}-x-2=0" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow\left(x-2\right)\left(x+1\right)=0" title="\Rightarrow\left(x-2\right)\left(x+1\right)=0" /></p><p><span> </span><img src="https://latex.codecogs.com/svg.image?\left(x-2\right)=0\,\,\textrm{atau}\,\,\left(x+1\right)=0" title="\left(x-2\right)=0\,\,\textrm{atau}\,\,\left(x+1\right)=0" /></p><p><span> </span><span> <span> </span></span><img src="https://latex.codecogs.com/svg.image?x=2" title="x=2" /> <img src="https://latex.codecogs.com/svg.image?x=-1" title="x=-1" /></p><p><br /></p><p>18. <img src="https://latex.codecogs.com/svg.image?9^{3x+2}=\frac{1}{3^{2x-5}}" title="9^{3x+2}=\frac{1}{3^{2x-5}}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?9^{3x+2}=\frac{1}{3^{2x-5}}" title="9^{3x+2}=\frac{1}{3^{2x-5}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(3^{2}\right)^{3x+2}=3^{-\left(2x-5\right)}" title="\Leftrightarrow\left(3^{2}\right)^{3x+2}=3^{-\left(2x-5\right)}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;3^{6x+4}=3^{-2x+5}" title="\Leftrightarrow 3^{6x+4}=3^{-2x+5}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;6x+4=-2x+5" title="\Rightarrow 6x+4=-2x+5" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;6x+2x=5-4" title="\Rightarrow 6x+2x=5-4" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;8x=1" title="\Rightarrow 8x=1" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{1}{8}" title="\Rightarrow x=\frac{1}{8}" /></p><p><br /></p><p>19. <img src="https://latex.codecogs.com/svg.image?\sqrt{9^{2x+4}}=\left(\frac{1}{3}\right)^{-3x-3}" title="\sqrt{9^{2x+4}}=\left(\frac{1}{3}\right)^{-3x-3}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?\sqrt{9^{2x+4}}=\left(\frac{1}{3}\right)^{-3x-3}" title="\sqrt{9^{2x+4}}=\left(\frac{1}{3}\right)^{-3x-3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(9^{2x+4}\right)^{\frac{1}{2}}=\left(3^{-1}\right)^{-3x-3}" title="\Leftrightarrow\left(9^{2x+4}\right)^{\frac{1}{2}}=\left(3^{-1}\right)^{-3x-3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(\left(3^{2}\right)^{2x+4}\right)^{\frac{1}{2}}=3^{3x+3}" title="\Leftrightarrow\left(\left(3^{2}\right)^{2x+4}\right)^{\frac{1}{2}}=3^{3x+3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(3^{4x+8}\right)^{\frac{1}{2}}=3^{3x+3}" title="\Leftrightarrow\left(3^{4x+8}\right)^{\frac{1}{2}}=3^{3x+3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;3^{2x+4}=3^{3x+3}" title="\Leftrightarrow 3^{2x+4}=3^{3x+3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x+4=3x+3" title="\Rightarrow 2x+4=3x+3" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;2x-3x=3-4" title="\Rightarrow 2x-3x=3-4" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow-x=-1" title="\Rightarrow-x=-1" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=1" title="\Rightarrow x=1" /></p><p><br /></p><p>20. <img src="https://latex.codecogs.com/svg.image?\left(\frac{1}{4}\right)^{x-1}=\sqrt[3]{2^{3x+1}}" title="\left(\frac{1}{4}\right)^{x-1}=\sqrt[3]{2^{3x+1}}" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?\left(\frac{1}{4}\right)^{x-1}=\sqrt[3]{2^{3x+1}}" title="\left(\frac{1}{4}\right)^{x-1}=\sqrt[3]{2^{3x+1}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(4^{-1}\right)^{x-1}=\left(2^{3x+1}\right)^{\frac{1}{3}}" title="\Leftrightarrow\left(4^{-1}\right)^{x-1}=\left(2^{3x+1}\right)^{\frac{1}{3}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(\left(2^{2}\right)^{-1}\right)^{x-1}=2^{\frac{3x+1}{3}}" title="\Leftrightarrow\left(\left(2^{2}\right)^{-1}\right)^{x-1}=2^{\frac{3x+1}{3}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow\left(2^{-2}\right)^{x-1}=2^{\frac{3x+1}{3}}" title="\Leftrightarrow\left(2^{-2}\right)^{x-1}=2^{\frac{3x+1}{3}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{-2x+2}=2^{\frac{3x+1}{3}}" title="\Leftrightarrow 2^{-2x+2}=2^{\frac{3x+1}{3}}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow-2x+2=\frac{3x+1}{3}" title="\Rightarrow-2x+2=\frac{3x+1}{3}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow-6x+6=3x+1" title="\Rightarrow-6x+6=3x+1" /></p><p><img src="https://latex.codecogs.com/svg.image?\Rightarrow-6x-3x=1-6" title="\Rightarrow-6x-3x=1-6" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow-9x=-5" title="\Rightarrow-9x=-5" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x=\frac{5}{9}" title="\Rightarrow x=\frac{5}{9}" /></p><p><br /></p><p>21. <img src="https://latex.codecogs.com/svg.image?2^{x-x^{2}}=1" title="2^{x-x^{2}}=1" /></p><p>
Pembahasan</p><p><img src="https://latex.codecogs.com/svg.image?2^{x-x^{2}}=1" title="2^{x-x^{2}}=1" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Leftrightarrow&space;2^{x-x^{2}}=2^{0}" title="\Leftrightarrow 2^{x-x^{2}}=2^{0}" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x-x^{2}=0" title="\Rightarrow x-x^{2}=0" /></p><p>
<img src="https://latex.codecogs.com/svg.image?\Rightarrow&space;x\left(1-x\right)=0" title="\Rightarrow x\left(1-x\right)=0" /></p><p><span> </span><img src="https://latex.codecogs.com/svg.image?x=0\,\,\textrm{atau}\,\,\left(1-x\right)=0" title="x=0\,\,\textrm{atau}\,\,\left(1-x\right)=0" /></p><p>
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?x=1" title="x=1" /></p><p>Demikian pembahasan soal persamaan eksponen ini, semoga bermanfaat. Terimakasih.</p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-41207136364748815442023-09-21T09:49:00.000+08:002023-09-21T09:49:38.962+08:00Langkah-Langkah Menentukan Jarak Titik Ke Garis Pada Bangun Ruang<p style="text-align: justify;">Jarak pada bangun ruang merupakan salah satu materi pokok pada mata pelajaran Matematika Wajib Kelas XII SMA/MA semua jurusan pada kurikulum 2013. Sebelum menghitung jarak ke garis pada bangun ruang terlebih dahulu harus menentukan ruas garis yang merupakan jarak titik ke garis tersebut. Pada postingan kali ini akan membahas langkah-langkah menentukan jarak titik ke garis pada bangun ruang.</p><h3 style="text-align: justify;">LANGKAH-LANGKAH MENENTUKAN JARAK TITIK KE GARIS PADA BANGUN RUANG</h3><p style="text-align: justify;">Untuk membahas langkah-langkah ini akan diberikan beberapa contoh sebagai berikut.</p><p style="text-align: justify;">Soal 1. Sebuah kubus ABCD.EFGH dengan panjang rusuk 6 cm. Tentukan jarak titik B ke garis AF.</p><p style="text-align: justify;"><b>Pembahasan</b></p><p style="text-align: justify;"><b>Langkah-langkah</b></p><p style="text-align: justify;">1. Gambarlah kubus ABCD.EFGH dengan panjang rusu 6 cm, seperti gambar berikut.</p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjU1PMYCnNIttKW8FBc9tB17Yd17yfrJXVlEfrnvFu6EOM51__zWlfvHC-rUMWw_lX7CaLwW_D0xUmjoiu2HhqWApgLWTrq2TVOHy6AwRyrGkTaDWvWWvWI4j0OkfgnY2f2gx9v9yZSnCyo5XzGxHfGKxqRn3rw79DqUIk5PcQBb_qxGYvhIkq8oJAVfDA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="538" data-original-width="545" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjU1PMYCnNIttKW8FBc9tB17Yd17yfrJXVlEfrnvFu6EOM51__zWlfvHC-rUMWw_lX7CaLwW_D0xUmjoiu2HhqWApgLWTrq2TVOHy6AwRyrGkTaDWvWWvWI4j0OkfgnY2f2gx9v9yZSnCyo5XzGxHfGKxqRn3rw79DqUIk5PcQBb_qxGYvhIkq8oJAVfDA" width="243" /></a></div>2. Gambarlah garis atau ruas garis AF, seperti gambar berikut.<p></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi0q526gCyUWhMQTQbcaSpy2FPpAmVVT3O4ZAVrd2IcTnVIMdPR8dMXbHIh1BF39INTxiq338NykKh5QS4UOsIzPP_wCFZBQcOkXsTkWxvjqu6OLzoALstdYvsGym6SiGJWbjCD42koXsPZ-IPqoD-EWXIeq8jQEeVLPa0HE9Dsc7PkII-HuplbRG-rlg0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="521" data-original-width="527" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEi0q526gCyUWhMQTQbcaSpy2FPpAmVVT3O4ZAVrd2IcTnVIMdPR8dMXbHIh1BF39INTxiq338NykKh5QS4UOsIzPP_wCFZBQcOkXsTkWxvjqu6OLzoALstdYvsGym6SiGJWbjCD42koXsPZ-IPqoD-EWXIeq8jQEeVLPa0HE9Dsc7PkII-HuplbRG-rlg0" width="243" /></a></div>3. Buat proyeksi titik B pada garis AF, misal titik P, seperti gambar berikut.<p></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEidiO_8R5j10Bb73lNIZJG5ETh_N4RnZIe3BA-Am_8zquGIx-_oUaQpuQmXLv7oTImJUs4qopmlsjPZB9QNwUqgS6eZdz52qL3a1zJ4N2wHDqp3pBFxiBmn22rQEzGLv2hb0Khu_F04zK3eAaxir46BeYPgXKZN5eRQXFOSGXDdFOKd7QAaXOVP1E4oii8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="518" data-original-width="523" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEidiO_8R5j10Bb73lNIZJG5ETh_N4RnZIe3BA-Am_8zquGIx-_oUaQpuQmXLv7oTImJUs4qopmlsjPZB9QNwUqgS6eZdz52qL3a1zJ4N2wHDqp3pBFxiBmn22rQEzGLv2hb0Khu_F04zK3eAaxir46BeYPgXKZN5eRQXFOSGXDdFOKd7QAaXOVP1E4oii8" width="242" /></a></div>4. Buat ruas garis dari titik B ke titik P dimana BP tegak lurus AF<p></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi-f056Ws2fyGy_0kU4XETl5aelIVp5n3IuH3OUxldfwln05U3s0fbqyHJaTAtVFUI-cJLdoByEcqnxWQEQtwMcI8S5Dgu3zcGlh15HJkUSQ84Ozlpm1YQTDNEeT91R9-lROl2QbX60rw0eSFlQ80DhiYxf2gJ6MmcoZzN-VXSjOFnOX4Q-y0b7PMtPMwI" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="539" data-original-width="528" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEi-f056Ws2fyGy_0kU4XETl5aelIVp5n3IuH3OUxldfwln05U3s0fbqyHJaTAtVFUI-cJLdoByEcqnxWQEQtwMcI8S5Dgu3zcGlh15HJkUSQ84Ozlpm1YQTDNEeT91R9-lROl2QbX60rw0eSFlQ80DhiYxf2gJ6MmcoZzN-VXSjOFnOX4Q-y0b7PMtPMwI" width="235" /></a></div>5. Jadi jarak titik B ke garis AF adalah panjang ruas garis BP.<p></p><p style="text-align: justify;">6. Menghitung panjang ruas garis BP, bisa menggunakan teorema pythagoras, luas segitiga atau aturan cosinus. Pada perhitungan kali ini menggunakan luas segitiga.</p><p style="text-align: justify;">Perhatikan segitiga ABF</p><p style="text-align: justify;">Diketahui:</p><p style="text-align: justify;">AB = 6 cm</p><p style="text-align: justify;">BF = 6 cm</p><p style="text-align: justify;">AF = panjang diagonal bidang kubus = <img src="https://latex.codecogs.com/svg.image?6\sqrt{2}" style="text-align: left;" title="6\sqrt{2}" /> cm</p><p style="text-align: justify;"><span style="text-align: left;"></span>Maka</p><p style="text-align: justify;"><img src="https://latex.codecogs.com/svg.image?&space;BP=\frac{AB&space;x&space;BF}{AF}" style="text-align: left;" title="BP=\frac{AB x BF}{AF}" /></p><p style="text-align: justify;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{6&space;x&space;6}{6\sqrt{2}}" style="text-align: left;" title="=\frac{6 x 6}{6\sqrt{2}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{6}{\sqrt{2}}" style="text-align: left;" title="=\frac{6}{\sqrt{2}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{6}{2}\sqrt{2}" style="text-align: left;" title="=\frac{6}{2}\sqrt{2}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=3\sqrt{2}" style="text-align: left;" title="=3\sqrt{2}" /><span style="text-align: left;"> </span></p><p style="text-align: justify;">7. Jadi jarak titik B ke garis AF adalah <img src="https://latex.codecogs.com/svg.image?3\sqrt{2}" title="3\sqrt{2}" /> cm <img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="\blacksquare" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;">Soal 2. Sebuat Limas beraturan T.ABCD dengan panjang rusuk alas 4 cm dan tinggi 3 cm. Tentukan jarak titik A ke garis TC</p><p style="text-align: justify;">Pembahasan</p><p style="text-align: justify;">Langkah-langkah</p><p style="text-align: justify;">1. Buatlah gambar limas beraturan T.ABCD sesuai soal, seperti gambar berikut</p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg0MPPIkrFBKfUJLNPhBsctOxERxl7zFmcIdsNZHPUCAAiXgup_J5IIH4JQwcsZyI-tlRhOMQbWSiBjZNBTDTqJW_K3UPBxHfSzo5aEhuyHEQwcW03LoVk5EsgXOmcqhW-WJKn1Kj9h1K5KgBZ3Mp7wRbpATfvfWI0DIE3c48uvtw_pztVlL9ufiNmsxwY" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="498" data-original-width="701" height="227" src="https://blogger.googleusercontent.com/img/a/AVvXsEg0MPPIkrFBKfUJLNPhBsctOxERxl7zFmcIdsNZHPUCAAiXgup_J5IIH4JQwcsZyI-tlRhOMQbWSiBjZNBTDTqJW_K3UPBxHfSzo5aEhuyHEQwcW03LoVk5EsgXOmcqhW-WJKn1Kj9h1K5KgBZ3Mp7wRbpATfvfWI0DIE3c48uvtw_pztVlL9ufiNmsxwY" width="320" /></a></div>2. Tentukan proyeksi titik A pada garis TC misal titik Q, seperti gambar berikut<p></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEibA8UCHIy-LCfUKQs0L9gPpUvjrIQcesH7I_iAvAn0XtvWs02cWoTfNdL8m4AmgRcWw2XyoEXqn0mar-KvxD961O-z4I-s68VDIx4IOxYOHeycHhpoZU3TT5CcLGNyWIfqfM9ivx6RQojAiriPR4FN8I6dNQSbkvN4Rn5zMt9CZ-KHXHtGjKOZ30r2als" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="487" data-original-width="634" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEibA8UCHIy-LCfUKQs0L9gPpUvjrIQcesH7I_iAvAn0XtvWs02cWoTfNdL8m4AmgRcWw2XyoEXqn0mar-KvxD961O-z4I-s68VDIx4IOxYOHeycHhpoZU3TT5CcLGNyWIfqfM9ivx6RQojAiriPR4FN8I6dNQSbkvN4Rn5zMt9CZ-KHXHtGjKOZ30r2als" width="312" /></a></div><br />3. Buat ruas garis dari titik A ke titik Q, seperti gambar berikut.<p></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg5dl6fwTOBQlfcrP_7Q1_XWvzuFUnjpjWpVNDCK1IiC7rfUqlcGGM7x1JkaF9gVUGaMqWgqyZ7Volc3N984Nyy7SZWYyoL05YggL80A1mE-xgYXV2k6aYAgXyHHJwsjUOid_6NniMNU21-2RfBYFqN_lqRWwnowy2Nxk0vtmOeeYWUAtav8WB1M6H2-u0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="516" data-original-width="667" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEg5dl6fwTOBQlfcrP_7Q1_XWvzuFUnjpjWpVNDCK1IiC7rfUqlcGGM7x1JkaF9gVUGaMqWgqyZ7Volc3N984Nyy7SZWYyoL05YggL80A1mE-xgYXV2k6aYAgXyHHJwsjUOid_6NniMNU21-2RfBYFqN_lqRWwnowy2Nxk0vtmOeeYWUAtav8WB1M6H2-u0" width="310" /></a></div>4. Jadi jarak titik A ke garis TC adalah panjang ruas garis AQ.<p></p><p style="text-align: justify;">5. Menghitung panjang ruas garis BP, bisa menggunakan teorema pythagoras, luas segitiga atau aturan cosinus. Pada perhitungan kali ini menggunakan luas segitiga.</p><p style="text-align: justify;">Perhatikan segitiga TAC</p><p style="text-align: justify;">Diketahui</p><p style="text-align: justify;">OT = 3 cm</p><p style="text-align: justify;">AC = <img src="https://latex.codecogs.com/svg.image?4\sqrt{2}" style="text-align: left;" title="4\sqrt{2}" /> cm</p><p style="text-align: justify;"><img src="https://latex.codecogs.com/svg.image?OC=\frac{1}{2}AC=\frac{1}{2}4\sqrt{2}=2\sqrt{2}" style="text-align: left;" title="OC=\frac{1}{2}AC=\frac{1}{2}4\sqrt{2}=2\sqrt{2}" /> cm</p><p style="text-align: justify;">Untuk menggunakan luas segitiga maka panjang TC harus diketahui, perhatikan segitiga TOC.</p><p style="text-align: justify;"><img src="https://latex.codecogs.com/svg.image?TC=\sqrt{OT^{2}+OC^{2}}" style="text-align: left;" title="TC=\sqrt{OT^{2}+OC^{2}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{3^{2}+\left(2\sqrt{2}\right)^{2}}" style="text-align: left;" title="=\sqrt{3^{2}+\left(2\sqrt{2}\right)^{2}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{9+8}" style="text-align: left;" title="=\sqrt{9+8}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{17}" style="text-align: left;" title="=\sqrt{17}" /></p><p style="text-align: justify;">Dari segitiga TAC diperoleh</p><p style="text-align: justify;"><img src="https://latex.codecogs.com/svg.image?AQ=\frac{AC&space;x&space;OT}{TC}" style="text-align: left;" title="AQ=\frac{AC x OT}{TC}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{4\sqrt{2}x&space;3}{\sqrt{17}}" style="text-align: left;" title="=\frac{4\sqrt{2}x 3}{\sqrt{17}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{12\sqrt{2}}{\sqrt{17}}" style="text-align: left;" title="=\frac{12\sqrt{2}}{\sqrt{17}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{12\sqrt{2}\sqrt{17}}{17}" style="text-align: left;" title="=\frac{12\sqrt{2}\sqrt{17}}{17}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{12\sqrt{34}}{17}" style="text-align: left;" title="=\frac{12\sqrt{34}}{17}" /></p><p style="text-align: justify;">6. Jadi jarak titik A ke garis TC adalah <img src="https://latex.codecogs.com/svg.image?\frac{12\sqrt{34}}{17}" style="text-align: left;" title="\frac{12\sqrt{34}}{17}" /> cm<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="\blacksquare" /></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-22836221166265836992023-01-10T15:12:00.002+08:002023-01-11T11:38:58.671+08:00KOMPOSISI TRANSFORMASI DENGAN MATRIKS DAN PEMBAHASAN SOAL<p style="text-align: justify;"><span style="font-size: medium;"><b>Komposisi Transformasi Dengan Matriks -</b> merupakan materi matematika wajib kelas XI semua jurusan yang merupakan kelanjutan dari materi komposisi transformasi geometri yang sudah diajarkan di SMP/MTs. Berikut penjelasan Komposisi Transformasi dengan Matriks.</span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi425pWBY2kIxNyg4wKp5h8Q4VKglg_i6o35toFmoBt2VVCwIGY-flbDgUllMjccgVr3QI0HYFb7C-jVoGqAwsIhB1vZ6dlu9pn72-qPx6zS5yRsjbU8_WhzmasfKLQvilaOq1gpmrNvdrYAcxZOGOjpoi2rw3s-fry4od7GFrjq_X1jDJWdqWn37q-/s1500/Biru%20Oranye%20dan%20Puti%20Elegan%20Perumahan%20Minimalis%20Tajuk%20Twitter%20(1).png" style="margin-left: auto; margin-right: auto;"><img alt="Komposisi Transformasi dengan Matriks" border="0" data-original-height="500" data-original-width="1500" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi425pWBY2kIxNyg4wKp5h8Q4VKglg_i6o35toFmoBt2VVCwIGY-flbDgUllMjccgVr3QI0HYFb7C-jVoGqAwsIhB1vZ6dlu9pn72-qPx6zS5yRsjbU8_WhzmasfKLQvilaOq1gpmrNvdrYAcxZOGOjpoi2rw3s-fry4od7GFrjq_X1jDJWdqWn37q-/w640-h213/Biru%20Oranye%20dan%20Puti%20Elegan%20Perumahan%20Minimalis%20Tajuk%20Twitter%20(1).png" title="Komposisi Transformasi dengan Matriks" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">sumber : www.google.com dan diseain menggunakan canva for education</td></tr></tbody></table><br /><span style="font-size: medium;"><br /></span><p></p><h3 style="text-align: left;"><span style="font-size: medium;">PENGERTIAN</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Misalkan suatu benda atau bangun dilakukan komposisi transformasi. Pertama ditansformasi <img src="https://latex.codecogs.com/svg.image?T_{1}" title="https://latex.codecogs.com/svg.image?T_{1}" /> yang bersesuaian dengan matriks <img src="https://latex.codecogs.com/svg.image?M_{1}" title="https://latex.codecogs.com/svg.image?M_{1}" />, dilanjutkan dengan transformasi <img src="https://latex.codecogs.com/svg.image?T_{2}" title="https://latex.codecogs.com/svg.image?T_{2}" /> yang bersesuaian dengan matriks <img src="https://latex.codecogs.com/svg.image?M_{2}" title="https://latex.codecogs.com/svg.image?M_{2}" />, dan dilanjutkan lagi dengan transformasi <img src="https://latex.codecogs.com/svg.image?T_{3}" title="https://latex.codecogs.com/svg.image?T_{3}" /> yang bersesuaian dengan matriks <img src="https://latex.codecogs.com/svg.image?M_{3}" title="https://latex.codecogs.com/svg.image?M_{3}" />. Penulisan komposisinya yaitu</span></p><p style="text-align: justify;"></p><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh5jqRmQvoQhTmpWab0cRMZDnLOCg8wTVX4ZZJpLc1C-yM3eNNLz9CMnitz86L7-50hiaXX0HiBE_Pe_Ww2-LJ2ZkBZZqKeCwaTHssyvPVpCFq2OWlU_V-Jei7jVM3eLm2KxAWfPQw7Gm8ZwYGr2oNKGGJy5U7w8YOXo1GEDkIAoDPMMqgyruqg7Qt3"><span style="font-size: medium;"><img alt="Komposisi Transformasi Dengan Matriks" data-original-height="64" data-original-width="271" height="55" src="https://blogger.googleusercontent.com/img/a/AVvXsEh5jqRmQvoQhTmpWab0cRMZDnLOCg8wTVX4ZZJpLc1C-yM3eNNLz9CMnitz86L7-50hiaXX0HiBE_Pe_Ww2-LJ2ZkBZZqKeCwaTHssyvPVpCFq2OWlU_V-Jei7jVM3eLm2KxAWfPQw7Gm8ZwYGr2oNKGGJy5U7w8YOXo1GEDkIAoDPMMqgyruqg7Qt3=w229-h55" title="Komposisi Transformasi Dengan Matriks" width="229" /></span></a></div><span style="font-size: medium;"><br /><span>Perlu diperhatikan bahwa penulisannya dibalik sesuai dengan urutan pengerjaannya.</span></span><p></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><h3 style="text-align: justify;"><span style="font-size: medium;">MENENTUKAN BAYANGAN</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Bentuk umum bayangan dari komposisi transformasi dengan matriks adalah</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhM5jbXFHqNflqB7lS-9ti9J0Ce6ONSP8-d-4u5il2kOGxbhkP6jDn2VNhYc_XuChFmRU8Jhu-cwoXXZf-1j6wedTfcKtLSxMhQi-PJasQIs6BrDxBkrLg1fql83aOXY9jaOP-o_40vgspZpv7uMvcGFv-WlXFkZldXoauOrpKxaJCR7oXkieKdBKya" style="margin-left: 1em; margin-right: 1em;"><img alt="Bentuk Umum Bayangan" data-original-height="68" data-original-width="326" height="51" src="https://blogger.googleusercontent.com/img/a/AVvXsEhM5jbXFHqNflqB7lS-9ti9J0Ce6ONSP8-d-4u5il2kOGxbhkP6jDn2VNhYc_XuChFmRU8Jhu-cwoXXZf-1j6wedTfcKtLSxMhQi-PJasQIs6BrDxBkrLg1fql83aOXY9jaOP-o_40vgspZpv7uMvcGFv-WlXFkZldXoauOrpKxaJCR7oXkieKdBKya=w244-h51" title="Bentuk Umum Bayangan" width="244" /></a></span></div><span style="font-size: medium;"><br />1. Bayangan dengan titik pusat O(0,0)</span><p></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjkHyVjqBJuHr-KjNk4usfj0Q9N9sBRn9qRG1mmbHyLiXTZ1rpOasv25BF7h6Oz29KOAO6tmcuIHBbabEmm_MOVrCQAbMQ9ql03zlhJgCiy-GVjuV7oc2F0q2PMQmIn9xLl4UOMSo_Fc0kJAWbo30iADdouUmyjNl2A98zF3jLUBSi7k-o_QL1N65xN" style="margin-left: 1em; margin-right: 1em;"><img alt="Bayangan dengan titik pusat O(0,0)" data-original-height="107" data-original-width="232" height="100" src="https://blogger.googleusercontent.com/img/a/AVvXsEjkHyVjqBJuHr-KjNk4usfj0Q9N9sBRn9qRG1mmbHyLiXTZ1rpOasv25BF7h6Oz29KOAO6tmcuIHBbabEmm_MOVrCQAbMQ9ql03zlhJgCiy-GVjuV7oc2F0q2PMQmIn9xLl4UOMSo_Fc0kJAWbo30iADdouUmyjNl2A98zF3jLUBSi7k-o_QL1N65xN=w215-h100" title="Bayangan dengan titik pusat O(0,0)" width="215" /></a></span></div><span style="font-size: medium;"><br />2. Bayangan dengan titik pusat P(a,b)</span><p></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEis_HvwE-NGMo9FUo7bjAVhAn_bWQOnmzvL6cHZ5IM3eH5Xk3IHspdCjx0sKycXUKzPGzlYNZSU6LMy1zl-_YnvFpZqxmd0tdGU1W8gY1lq7-7U8YSclo0UXrfg5ced8gerfsXbnqwSv5oN3olNVoc-aAQsJHUlzx8RB6ptx9iJMYShMXCRPJTtKkiT" style="margin-left: 1em; margin-right: 1em;"><img alt="Bayangan dengan titik P(a,b)" data-original-height="110" data-original-width="300" height="105" src="https://blogger.googleusercontent.com/img/a/AVvXsEis_HvwE-NGMo9FUo7bjAVhAn_bWQOnmzvL6cHZ5IM3eH5Xk3IHspdCjx0sKycXUKzPGzlYNZSU6LMy1zl-_YnvFpZqxmd0tdGU1W8gY1lq7-7U8YSclo0UXrfg5ced8gerfsXbnqwSv5oN3olNVoc-aAQsJHUlzx8RB6ptx9iJMYShMXCRPJTtKkiT=w289-h105" title="Bayangan dengan titik P(a,b)" width="289" /></a></span></div><span style="font-size: medium;"><br /></span><h3><span style="font-size: medium;">MATRIKS TRANSFORMASI (M)</span></h3><p></p><p style="text-align: justify;"><span style="font-size: medium;">Untuk memudahkan dalam pengerjaan masalah transformasi berikut diberikan matriks transformasi (M)</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Refleksi atau Pencerminan</span></h3><p style="text-align: justify;"><span style="font-size: medium;"><span>1. Matriks transformasi refleksi atau pencerminan t</span><span>erhadap pusat koordinat O(0,0)</span></span></p><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhkQyVKg2P_TAIjxlH-dR-t62aiVmjulc8kXdGy4GiLbcOd_6Ro7OuUWly4KzU5HF1z38GU3b7poY6U3GUj2fK7k7tVKVcX-DwOTdpnkh2Nc4l6tKlFI2QwR2D1_57t-s1_GHabY8lZ-sIyBwcAYKTvUKPm4gqwRNc7xzhJKWLRE2g4GVMlSMiV8Bmj" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Matriks Transformasi pencerminan terhadap titik pusat O(0,0)" data-original-height="52" data-original-width="152" height="50" src="https://blogger.googleusercontent.com/img/a/AVvXsEhkQyVKg2P_TAIjxlH-dR-t62aiVmjulc8kXdGy4GiLbcOd_6Ro7OuUWly4KzU5HF1z38GU3b7poY6U3GUj2fK7k7tVKVcX-DwOTdpnkh2Nc4l6tKlFI2QwR2D1_57t-s1_GHabY8lZ-sIyBwcAYKTvUKPm4gqwRNc7xzhJKWLRE2g4GVMlSMiV8Bmj=w145-h50" title="Matriks Transformasi pencerminan terhadap titik pusat O(0,0)" width="145" /></span></a></div><span style="font-size: medium;"><br /></span><p><span style="font-size: medium;">2. Matriks tranformasi refleksi atau pencerminan terhadap sumbu x</span></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEitjBeLBLZWEkCaQqoSLJoLVDyAYHnZUFi8N_EK83e5Cg8uxxK8CruxhP36ZIgUK8E4j7l1h7itRRJ15weMTK5uNrHOZ__K3nMCve4zLJtK13bg5Ri0d-3_EVZYH0lQbTEEsmc4tyYy8rdeDUOz83JXXLWi3wx3eNmbUmxv2iprPZqL4oDQL9vBlHgs" style="margin-left: 1em; margin-right: 1em;"><img alt="Matriks transformasi refleksi terhadap sumbu x" data-original-height="54" data-original-width="149" height="54" src="https://blogger.googleusercontent.com/img/a/AVvXsEitjBeLBLZWEkCaQqoSLJoLVDyAYHnZUFi8N_EK83e5Cg8uxxK8CruxhP36ZIgUK8E4j7l1h7itRRJ15weMTK5uNrHOZ__K3nMCve4zLJtK13bg5Ri0d-3_EVZYH0lQbTEEsmc4tyYy8rdeDUOz83JXXLWi3wx3eNmbUmxv2iprPZqL4oDQL9vBlHgs=w149-h54" title="Matriks transformasi refleksi terhadap sumbu x" width="149" /></a></span></div><span style="font-size: medium;"><span><br />3. </span><span>Matriks tranformasi r</span><span>efleksi atau pencerminan t</span><span>erhadap sumbu y</span></span><p></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgUb_VxXxOnVy0XRpIYZgMKPhEhHbZHoIz2d8NAHjGVFsOmAmT01-fK4Tofzb9o2njDW5S8fbefbImH5lyAWwgcppiSUx_6It6c5BBsXoKm1WZ_6gJdPzFkuYmRP9019aMUoX649k67BX6RxE_I_uJFl28Nodg49gMSsZfenA8SvVoriGdQQNgZl9Ng" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Matriks tranformasi refleksi terhadap sumbu y" data-original-height="50" data-original-width="148" height="51" src="https://blogger.googleusercontent.com/img/a/AVvXsEgUb_VxXxOnVy0XRpIYZgMKPhEhHbZHoIz2d8NAHjGVFsOmAmT01-fK4Tofzb9o2njDW5S8fbefbImH5lyAWwgcppiSUx_6It6c5BBsXoKm1WZ_6gJdPzFkuYmRP9019aMUoX649k67BX6RxE_I_uJFl28Nodg49gMSsZfenA8SvVoriGdQQNgZl9Ng=w150-h51" title="Matriks tranformasi refleksi terhadap sumbu y" width="150" /></span></a></div><span style="font-size: medium;"><br /><span>4. </span><span>Matriks tranformasi r</span><span>efleksi atau pencerminan t</span><span>erhadap garis y = x</span></span><p></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh90uFJC5kXq_hddN5wifWcJe-hIof85gCiO4fn5HnvAd0P5LDw8ZvIUbjHZx8Q3wsl1xCS2bJ0Z9ymGl3smjNzgqWs28onoPjrOQ0zP4sRst-aoMT32sAlXLnBiAG_NTsjnoqr0dmCfR_EnJ80A5RzIwAGAucZ7aynPl72Nzs4QiZvDGQ33pM-vuh8" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Matriks tranformasi refleksi terhadap garis y = x" data-original-height="51" data-original-width="138" height="54" src="https://blogger.googleusercontent.com/img/a/AVvXsEh90uFJC5kXq_hddN5wifWcJe-hIof85gCiO4fn5HnvAd0P5LDw8ZvIUbjHZx8Q3wsl1xCS2bJ0Z9ymGl3smjNzgqWs28onoPjrOQ0zP4sRst-aoMT32sAlXLnBiAG_NTsjnoqr0dmCfR_EnJ80A5RzIwAGAucZ7aynPl72Nzs4QiZvDGQ33pM-vuh8=w146-h54" title="Matriks tranformasi refleksi terhadap garis y = x" width="146" /></span></a></div><span style="font-size: medium;"><br /><span>5. </span><span>Matriks tranformasi r</span><span>efleksi atau pencerminan t</span><span>erhadap garis y = -x</span></span><p></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgpM2m9g1G-vLV7KID1jDwUqAMl52MFLngd5KkCC0zMQYH_Nc02EzXfUUI7NJaIHs4RJbrSvOjqvJVUI088paU_Ia6nBVF2NxoVWIJkUVZbqMqUWsX-rJjPHl5N9CHsBsFeVGdu656fJGl8lzP72pcg_IMMkQVmr2ZC5SyFqIFv8AAci7UqnwRbp1Al" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Matriks tranformasi refleksi terhadap garis y = -x" data-original-height="44" data-original-width="151" height="45" src="https://blogger.googleusercontent.com/img/a/AVvXsEgpM2m9g1G-vLV7KID1jDwUqAMl52MFLngd5KkCC0zMQYH_Nc02EzXfUUI7NJaIHs4RJbrSvOjqvJVUI088paU_Ia6nBVF2NxoVWIJkUVZbqMqUWsX-rJjPHl5N9CHsBsFeVGdu656fJGl8lzP72pcg_IMMkQVmr2ZC5SyFqIFv8AAci7UqnwRbp1Al=w155-h45" title="Matriks tranformasi refleksi terhadap garis y = -x" width="155" /></span></a></div><span style="font-size: medium;"><br /><span>6. </span><span>Matriks tranformasi r</span><span>efleksi atau pencerminan t</span><span>erhadap garis y = mx + c</span></span><p></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh-C6zhmqrK4VsgtQwWlJRLTNYiMWP6yKC-S3YTXFmX1ZbGZ8Ljk1DVm5ETJuKUkkfuRA13pFjx9rQRvLTWzBIgSJZXw-oxkSS2uW6kxi3u5L7jEr3xlvQr9t5rtzaSt7TrscN3IiTrei2uqKyfFMFUR8nEowC-1on9BErmQ9Rd6dOPtEWzMYKSZr0f" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Matriks tranformasi refleksi terhadap garis y = mx + c" data-original-height="55" data-original-width="197" height="56" src="https://blogger.googleusercontent.com/img/a/AVvXsEh-C6zhmqrK4VsgtQwWlJRLTNYiMWP6yKC-S3YTXFmX1ZbGZ8Ljk1DVm5ETJuKUkkfuRA13pFjx9rQRvLTWzBIgSJZXw-oxkSS2uW6kxi3u5L7jEr3xlvQr9t5rtzaSt7TrscN3IiTrei2uqKyfFMFUR8nEowC-1on9BErmQ9Rd6dOPtEWzMYKSZr0f=w200-h56" title="Matriks tranformasi refleksi terhadap garis y = mx + c" width="200" /></span></a></div><span style="font-size: medium;"><br /></span><h3><span style="font-size: medium;">Translasi</span></h3><p></p><p><span style="font-size: medium;">Matriks transformasi dari translasi adalah :</span></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiBg-Dhtirc3RpXh5Lu3eLmB7idGE0GBef3qh2_PnOxqY43UTXbpJRrGKxDUu00Ttr2mWckzWteitLaGCCDXiS-u6KaainxUUdIE7AGUMBqXpHkTPR_Smy9N-KMAKTl45evVZBF5IFB5CEchPFjMjC5IP2VtuhwBs_ihzRgmLupR1xBcmZvYyF3BH3n" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Matriks transformasi dari translasi" data-original-height="48" data-original-width="99" height="50" src="https://blogger.googleusercontent.com/img/a/AVvXsEiBg-Dhtirc3RpXh5Lu3eLmB7idGE0GBef3qh2_PnOxqY43UTXbpJRrGKxDUu00Ttr2mWckzWteitLaGCCDXiS-u6KaainxUUdIE7AGUMBqXpHkTPR_Smy9N-KMAKTl45evVZBF5IFB5CEchPFjMjC5IP2VtuhwBs_ihzRgmLupR1xBcmZvYyF3BH3n=w103-h50" title="Matriks transformasi dari translasi" width="103" /></span></a></div><span style="font-size: medium;"><br /></span><h3><span style="font-size: medium;">Rotasi</span></h3><p></p><p><span style="font-size: medium;"><span>Matriks transformasi dari rotasi dengan besar sudut </span><img src="https://latex.codecogs.com/svg.image?\theta&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\theta" /> adalah :</span></p><p><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh8SwdSUzCPrZJP4-kkzCRCQWCIrlnI0ZudQP2Eq2RGgJYxbuOUqTVG7VTvc5Sl_4taeu2N-AHMRaefAnFTHGYHFjI9x-Pu6uYfx-RjssC5bOiZt7kBwZIo63dlL_zABe5T3_GzvoyP-AcYeAHxVxF2Zmn5_NwUnrQ54jlnAc0zXPj-AmxeDVQNu-n6" style="margin-left: 1em; margin-right: 1em;"><img alt="Matriks transformasi dari rotasi dengan besar sudut tertentu" data-original-height="52" data-original-width="200" height="52" src="https://blogger.googleusercontent.com/img/a/AVvXsEh8SwdSUzCPrZJP4-kkzCRCQWCIrlnI0ZudQP2Eq2RGgJYxbuOUqTVG7VTvc5Sl_4taeu2N-AHMRaefAnFTHGYHFjI9x-Pu6uYfx-RjssC5bOiZt7kBwZIo63dlL_zABe5T3_GzvoyP-AcYeAHxVxF2Zmn5_NwUnrQ54jlnAc0zXPj-AmxeDVQNu-n6=w200-h52" title="Matriks transformasi dari rotasi dengan besar sudut tertentucom/svg.image?\theta" width="200" /></a></span></div><span style="font-size: medium;"><br /></span><h3><span style="font-size: medium;">Dilatasi</span></h3><p></p><p><span style="font-size: medium;"><span>Matriks transformasi dari dilatasi dengan faktor skala <i>k</i></span><span> adalah :</span></span></p><p><span style="font-size: medium;"></span></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgC3HB1eElBOiKB5Wa9BrbgPgNrNycjoUCpBIx9fNaAypM1g_4YzjHilYluSxJT10w_AM8oT9FVzIyAzQbcwoesGI_GWfStCU9wDndOda4XziBDg6Wy-6NNVz6stn-1HDAJ2SMvCaslXh5EywhOULTmHMAR8uvJkjdfP5dP1ejTwuigUnEFrKXxsGER" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Matriks transformasi dari dilatasi dengan faktor skala k" data-original-height="49" data-original-width="136" height="52" src="https://blogger.googleusercontent.com/img/a/AVvXsEgC3HB1eElBOiKB5Wa9BrbgPgNrNycjoUCpBIx9fNaAypM1g_4YzjHilYluSxJT10w_AM8oT9FVzIyAzQbcwoesGI_GWfStCU9wDndOda4XziBDg6Wy-6NNVz6stn-1HDAJ2SMvCaslXh5EywhOULTmHMAR8uvJkjdfP5dP1ejTwuigUnEFrKXxsGER=w146-h52" title="Matriks transformasi dari dilatasi dengan faktor skala k" width="146" /></span></a></p><span style="font-size: medium;"><br /></span><h3><span style="font-size: medium;">SYARAT MATRIKS TRANSFORMASI BISA LANGSUNG DIKALIKAN</span></h3><p><span style="font-size: medium;">Syarat supaya dua atau lebih matriks transformasi bisa dikalikan dan tidak mengerjakannya satu persatu adalah sebagai berikut.</span></p><p><span style="font-size: medium;">1. Matriks transformasinya harus berordo 2 x 2.</span></p><p><span style="font-size: medium;">2. Jika memiliki pusat (titik acuan seperti rotasi dan dilatasi), maka titik pusatnya harus sama.</span></p><p><span style="font-size: medium;">3. Jika pada transformasi tidak disebutkan titik pustnya seperti refleksi, maka titik pusatnya dianggap O(0,0) dan matriks transformasinya langsung dapat dikalikan dengan matriks transformasi yang titik pusatnya O(0,0) juga atau yang tidak disebutkan titik pusatnya.</span></p><p><span style="font-size: medium;"><b><u><i>Catatan</i></u></b></span></p><p><span style="font-size: medium;">Ketiga syarat diatas harus terpenuhi untuk bisa langsung mengalikan dua jenis matriks transformasi atau lebih.</span></p><p><span style="font-size: medium;"><b><br /></b></span></p><p><span style="font-size: medium;"><b>Contoh Soal dan Pembahasan</b></span></p><p><span style="font-size: medium;"><span>1. </span><span>Persamaan garis 3x – 2y dicerminkan terhadap sumbu x, kemudian dilanjutkan dengan rotasi sejauh </span><img src="https://latex.codecogs.com/svg.image?180^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?180^{o}" /><span> searah jarum jam, dan dilanjutkan lagi dengan dilatasi dengan faktor skala -3. Tentukan bayangan dari persamaan garis tersebut.</span></span></p><p><span style="font-size: medium;">Pembahasan</span></p><p><span style="font-size: medium;">Matriks dicerminkan terhadap sumbu x, rotasi dan dilatasi pasti berordo 2 x 2. Pada soal juga tidak disebutkaan titik pusat transformasinya, sehingga titik pusatnya dianggap sama yaitu O(0,0). Ini artinya ketiga matriks transformasi dapat dikalikan langsung tanpa harus mengerjakan satu persatu.</span></p><p></p><p><span style="font-size: medium;">a. Menentukan matriks transformasi masing-masing</span></p><p></p></div>
<p style="text-align: justify;"><span style="font-size: medium;"><span><img src="https://latex.codecogs.com/svg.image?T_{1}" title="https://latex.codecogs.com/svg.image?T_{1}" /> : percerminan terhadap sumbu x, maka </span><img src="https://latex.codecogs.com/svg.image?M_{1}=&space;\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;-1&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?M_{1}= \begin{pmatrix}1 & 0 \\0 & -1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?T_{2}" title="https://latex.codecogs.com/svg.image?T_{2}" /> : Rotasi sejauh <img src="https://latex.codecogs.com/svg.image?180^{o}" title="https://latex.codecogs.com/svg.image?180^{o}" /> terhadap sumbu x, maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?M_{2}=&space;\begin{pmatrix}cos(-180^{o})&space;&&space;-sin(-180^{o})&space;\\sin&space;(-180^{o})&space;&&space;cos&space;(-180^{o})&space;\\\end{pmatrix}=\begin{pmatrix}-1&space;&&space;0&space;\\0&space;&&space;-1&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?M_{2}= \begin{pmatrix}cos(-180^{o}) & -sin(-180^{o}) \\sin (-180^{o}) & cos (-180^{o}) \\\end{pmatrix}=\begin{pmatrix}-1 & 0 \\0 & -1 \\\end{pmatrix}" /> </span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?T_{3}" title="https://latex.codecogs.com/svg.image?T_{3}" /> : dilatasi dengan faktor skala -3, maka <img src="https://latex.codecogs.com/svg.image?M_{3}=\begin{pmatrix}-3&space;&&space;0&space;\\0&space;&&space;-3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?M_{3}=\begin{pmatrix}-3 & 0 \\0 & -3 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">b. Menentukan bayangan</span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}x'&space;\\&space;y'\end{pmatrix}=\left&space;(&space;M_{3}.M_{2}.M_{1}&space;\right&space;)\begin{pmatrix}x&space;\\&space;y\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}x' \\ y'\end{pmatrix}=\left ( M_{3}.M_{2}.M_{1} \right )\begin{pmatrix}x \\ y\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-3&space;&&space;0&space;\\0&space;&&space;-3&space;\\\end{pmatrix}\begin{pmatrix}-1&space;&&space;0&space;\\0&space;&&space;-1&space;\\\end{pmatrix}\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;-1&space;\\\end{pmatrix}\begin{pmatrix}x&space;\\&space;y\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-3 & 0 \\0 & -3 \\\end{pmatrix}\begin{pmatrix}-1 & 0 \\0 & -1 \\\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & -1 \\\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3&space;&&space;0&space;\\0&space;&&space;3&space;\\\end{pmatrix}\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;-1&space;\\\end{pmatrix}\begin{pmatrix}x&space;\\&space;y\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3 & 0 \\0 & 3 \\\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & -1 \\\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3&space;&&space;0&space;\\0&space;&&space;-3&space;\\\end{pmatrix}\begin{pmatrix}x&space;\\&space;y\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3 & 0 \\0 & -3 \\\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3x&space;\\&space;-3y\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3x \\ -3y\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Sehingga diperoleh :</span></p>
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?x'=3x\,&space;\rightarrow&space;x=\frac{1}{3}x'" title="https://latex.codecogs.com/svg.image?x'=3x\, \rightarrow x=\frac{1}{3}x'" /></span><div>
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?y'=-3y\,&space;\rightarrow&space;y=-\frac{1}{3}y'" title="https://latex.codecogs.com/svg.image?y'=-3y\, \rightarrow y=-\frac{1}{3}y'" /></span></div><p style="text-align: justify;"><span style="font-size: medium;">Substitusikan nilai x dan y ke persamaan garis yang akan dicari bayangannya</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?3x-2y=1" title="https://latex.codecogs.com/svg.image?3x-2y=1" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?3\left&space;(&space;\frac{1}{3}x'&space;\right&space;)-2\left&space;(&space;-\frac{1}{3}y'&space;\right&space;)=1" title="https://latex.codecogs.com/svg.image?3\left ( \frac{1}{3}x' \right )-2\left ( -\frac{1}{3}y' \right )=1" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?x'+\frac{2}{3}y'=1" title="https://latex.codecogs.com/svg.image?x'+\frac{2}{3}y'=1" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?3x'+2y'=3" title="https://latex.codecogs.com/svg.image?3x'+2y'=3" /></span></p><p style="text-align: justify;">
<span style="font-size: medium;">Jadi persamaan bayangan garis yang ditanyakan adalah <img src="https://latex.codecogs.com/svg.image?3x+2y=3\,&space;\,&space;\blacksquare&space;" title="https://latex.codecogs.com/svg.image?3x+2y=3\, \, \blacksquare" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>2. Tentukan persamaan bayangan </span><img src="https://latex.codecogs.com/svg.image?y=x^{2}+3" title="https://latex.codecogs.com/svg.image?y=x^{2}+3" /> jika ditranslasi sejauh <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1&space;\\&space;2\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1 \\ 2\end{pmatrix}" /> dan dilanjutkan dengan pencerminan terhadap garis y = - x</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Matriks translasi tidak berordo 2 x 2, sehingga tidak memenuhi syarat untuk melakukan perkalian langsung kedua matriks transformasinya. Ini artinya kita akan mengerjakan satu persatu.</span></p><p style="text-align: justify;"><span style="font-size: medium;">a. Pertama di ditranslasi</span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}x'&space;\\&space;y'\end{pmatrix}=\begin{pmatrix}x-2&space;\\&space;y+2\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}x' \\ y'\end{pmatrix}=\begin{pmatrix}x-2 \\ y+2\end{pmatrix}" /> </span></p><p style="text-align: left;"><span style="font-size: medium;">b. Kedua dicerminkan terhadap garis y = - x</span></p><p style="text-align: left;"><span style="font-size: medium;">Matriks transformasinya adalah<img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}0&space;&&space;-1&space;\\-1&space;&&space;0&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}0 & -1 \\-1 & 0 \\\end{pmatrix}" /> sehingga diperoleh :</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}x''&space;\\&space;y''\end{pmatrix}=\begin{pmatrix}0&space;&&space;-1&space;\\-1&space;&&space;0&space;\\\end{pmatrix}\begin{pmatrix}x-1&space;\\&space;y+2\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}x'' \\ y''\end{pmatrix}=\begin{pmatrix}0 & -1 \\-1 & 0 \\\end{pmatrix}\begin{pmatrix}x-1 \\ y+2\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-(y+2)&space;\\&space;-(x-1)\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-(y+2) \\ -(x-1)\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-y-2&space;\\&space;-x+1\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-y-2 \\ -x+1\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;">sehingga diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?x''=-y-2\rightarrow&space;y=-x''-2" title="https://latex.codecogs.com/svg.image?x''=-y-2\rightarrow y=-x''-2" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?y''=-x+1\rightarrow&space;x=-y''+1" title="https://latex.codecogs.com/svg.image?y''=-x+1\rightarrow x=-y''+1" /></span></p><p style="text-align: left;">
<span style="font-size: medium;">Substitusikan nilai x dan y ke persamaan garis yang akan dicari bayangannya</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?y=x^{2}+3" title="https://latex.codecogs.com/svg.image?y=x^{2}+3" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?-x''-2=\left&space;(&space;-y''+2&space;\right&space;)^{2}+3" title="https://latex.codecogs.com/svg.image?-x''-2=\left ( -y''+2 \right )^{2}+3" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?-x''-2=\left&space;(&space;y''&space;\right&space;)^{2}-2y''+1+3" title="https://latex.codecogs.com/svg.image?-x''-2=\left ( y'' \right )^{2}-2y''+1+3" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?-x''=\left&space;(&space;y''&space;\right&space;)^{2}-2y''+6" title="https://latex.codecogs.com/svg.image?-x''=\left ( y'' \right )^{2}-2y''+6" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?x''=-\left&space;(&space;y''&space;\right&space;)^{2}+2y''-6" title="https://latex.codecogs.com/svg.image?x''=-\left ( y'' \right )^{2}+2y''-6" /></span></p><p style="text-align: left;">
<span style="font-size: medium;">Jadi persamaan bayangan garis tersebut adalah <img src="https://latex.codecogs.com/svg.image?x=-y^{2}+2y-6\,&space;\,&space;\blacksquare&space;" title="https://latex.codecogs.com/svg.image?x=-y^{2}+2y-6\, \, \blacksquare" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Demikian pembahasan tentang komposisi transformasi dengan matriks dan pembahasan soal, semoga bermanfaat.</span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-3430049597051214762022-11-24T13:45:00.469+08:002022-11-29T13:50:51.802+08:00Cara Membuat Soal Interaktif di ClassPoint<h3 style="text-align: left;">Apa itu ClassPoint?</h3><p style="text-align: justify;"><span style="font-size: medium;"><b><i>Membuat Soal Interaktif di ClassPoint -</i></b> ClassPoint merupakan sebuah aplikasi Addons yang dikembangkan oleh perusahaan Inknoe yang memungkinkan setiap guru merancang dan menjalankan kuis secara langsung dan interaktif melalui Microsoft Power Point. Sebelum lanjut dan yang belum memahami cara install ClassPoint bisa dipelajari melalui <b><a href="https://www.sambimatika.my.id/2022/11/langkah-langkah-install-classpoint.html" target="_blank">link INI</a>.</b></span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLQtPJCwxFWLY3hnhPwpMsbFfsAQc06SA123dxj_vNiTMrGKDiyNJimrYAlhoR09C17SyIxdV9nyR-rKuOMgW069RW9DIPk-qE3dgJIbg5hsoZXz0s6hqHTxciE_UfbgnnaPx9GvZRMo0vOvs_QHY-VrirwPcPvPdBl0Xo4yn9WaFEFlkIqoSHOwgy/s400/pemanfaatan1.png" style="margin-left: auto; margin-right: auto;"><img alt="Addon ClassPoint" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLQtPJCwxFWLY3hnhPwpMsbFfsAQc06SA123dxj_vNiTMrGKDiyNJimrYAlhoR09C17SyIxdV9nyR-rKuOMgW069RW9DIPk-qE3dgJIbg5hsoZXz0s6hqHTxciE_UfbgnnaPx9GvZRMo0vOvs_QHY-VrirwPcPvPdBl0Xo4yn9WaFEFlkIqoSHOwgy/s16000/pemanfaatan1.png" title="Addon ClassPoint" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Classpont di Micrososft Power Point</td></tr></tbody></table><br /><span style="font-size: medium;"><br /></span><p></p><h3 style="text-align: justify;"><span style="font-size: medium;">Tipe soal apa saja yang dapat dibuat melalui Classpoint?</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Jenis-Jenis atau tipe soal kuis yang dapat dibuat menggunakan ClassPoint adalah :</span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Mulitiple Choice</span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Word Cloud</span></p><p style="text-align: justify;"><span style="font-size: medium;">3. Short Answer</span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Slide Drawing</span></p><p style="text-align: justify;"><span style="font-size: medium;">5. Image Upload</span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhVQwZslO3IntJcanF2DETXpBNR4Tz3NO2XWaDXkkdRrq_IPSTQvdaMErePWQlh5tTmudyx5n0WGGoZ3HBLks8GhQkJdRHwurD42F4JdM9WXsfUrpaHPq06BRXLo4flVk4ZUoDjv4sQrT-LZwedyVjY693DeAPkqWdnhd-t39htsz-o2K6kFGEUfGU/s472/pemanfaatan2.png" style="margin-left: auto; margin-right: auto;"><img alt="Ikon Interaktif Quiz Classpoint" border="0" data-original-height="200" data-original-width="472" height="136" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhVQwZslO3IntJcanF2DETXpBNR4Tz3NO2XWaDXkkdRrq_IPSTQvdaMErePWQlh5tTmudyx5n0WGGoZ3HBLks8GhQkJdRHwurD42F4JdM9WXsfUrpaHPq06BRXLo4flVk4ZUoDjv4sQrT-LZwedyVjY693DeAPkqWdnhd-t39htsz-o2K6kFGEUfGU/w320-h136/pemanfaatan2.png" title="Ikon Interaktif Quiz Classpoint" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Ikon interaktif kuis ClassPoint</td></tr></tbody></table><br /><span style="font-size: medium;">Selain itu ClassPoint juga memungkinkan guru untuk menggunakan fitur Annotation Setting seperti pensil dan white board dalam melakukan presentasi ke siswanya.</span><p></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfwtZKtmEuebz-35_wDClcxOLaiEPB631YdjzmQbJIjNpzAHuaz2CpFMLVMmEgU5GgwjBg9MJgLFF1iuViVzQOZqt9MYXaQM9mibU1LkdbKJnOhBHgRC59Sq6Y0GYcHN4TH-Dls5d0Cht0wU9NEKMOq9H5VNuSutFCf1JSXy7khDnEbSUvrvin8g0p/s587/pemanfaatan3.png" style="margin-left: auto; margin-right: auto;"><img alt="Annotation Setting" border="0" data-original-height="191" data-original-width="587" height="104" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfwtZKtmEuebz-35_wDClcxOLaiEPB631YdjzmQbJIjNpzAHuaz2CpFMLVMmEgU5GgwjBg9MJgLFF1iuViVzQOZqt9MYXaQM9mibU1LkdbKJnOhBHgRC59Sq6Y0GYcHN4TH-Dls5d0Cht0wU9NEKMOq9H5VNuSutFCf1JSXy7khDnEbSUvrvin8g0p/w320-h104/pemanfaatan3.png" title="Annotation Setting" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Annotation Setting ClassPoint</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><h3 style="text-align: justify;"><span style="font-size: medium;">Bagaimana Membuat Interaktif Kuis di ClassPoint?</span></h3><h4 style="text-align: justify;"><span style="font-size: medium;">A. Membuat Soal Multiple Choice</span></h4><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah membuat soal Multiple Choice</span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Buatlah soal pilihan ganda di Slide Power Point, misal seperti gambar berikut</span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1E2wEpWdHBk1hP1cg_kX0HGuTx7OtlGX0O8dKANnO3qTAEN6lZKxGVsyKg3pvWLkLORwI9pgPfqGxHUjYj2V_m2N9zaHW6VkSQLaQFal8VbL562JEJn-RPFcCaeJCk5NvN7E16ELd7pcNohWVvpNpMo7rAeI9YHd1unva8MOedchTfr7M2HMBh_EP/s400/pemanfaatan4.png" style="margin-left: auto; margin-right: auto;"><img alt="Soal Pilihan Ganda di Microsoft Power Point" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1E2wEpWdHBk1hP1cg_kX0HGuTx7OtlGX0O8dKANnO3qTAEN6lZKxGVsyKg3pvWLkLORwI9pgPfqGxHUjYj2V_m2N9zaHW6VkSQLaQFal8VbL562JEJn-RPFcCaeJCk5NvN7E16ELd7pcNohWVvpNpMo7rAeI9YHd1unva8MOedchTfr7M2HMBh_EP/s16000/pemanfaatan4.png" title="Soal Pilihan Ganda di Microsoft Power Point" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Membuat Soal Pilihan Ganda di Power Point</td></tr></tbody></table><br /><span style="font-size: medium;">2. Klik Menu <b>Inknoe ClassPoint</b>, Klik Tollbar <b>Multiple Choice</b>, dan lakukan pengaturan-pengaturan lanjutan, seperti gambar berikut.</span><p></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVAhzdErIE1yyMmWNGzfFAdUPEXfYFby_0b8ujNqk3Cs9LWx6oHQiWpMcfp7xeQdqsTSvDkSVKdmdNsB0w1icgE7Khl6ztj_z2luRUrrD908VQol_bkX4mT7pi5Pn7JSeuL1UpvXOCpZ4NFtigurB9NmE_nN2Zo0276H5AperWIkqUowNxqnpxirMs/s400/pemanfaatan5.png" style="margin-left: auto; margin-right: auto;"><img alt="Soal Interaktif Multiple Choice di ClassPoint" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVAhzdErIE1yyMmWNGzfFAdUPEXfYFby_0b8ujNqk3Cs9LWx6oHQiWpMcfp7xeQdqsTSvDkSVKdmdNsB0w1icgE7Khl6ztj_z2luRUrrD908VQol_bkX4mT7pi5Pn7JSeuL1UpvXOCpZ4NFtigurB9NmE_nN2Zo0276H5AperWIkqUowNxqnpxirMs/s16000/pemanfaatan5.png" title="Soal Interaktif Multiple Choice di ClassPoint" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Setting Soal tipe Multiple Choice</td></tr></tbody></table><br /><span style="font-size: medium;"><i><b>Keterangan Gambar</b></i></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Pada kotak <b>Interactive Quiz</b> :</span></p><p style="text-align: justify;"><b><i><span style="font-size: medium;">Question Type</span></i></b></p><p style="text-align: justify;"><span style="font-size: medium;">1. Pada kotak Drop Down tertulis <i><b>Multiple Choice</b></i> menunjukkan kita mau membuat soal pilihan ganda (Multiple Choice)</span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Klik 5, karena banyak pilihan jawaban soal (Option) 5 buah.</span></p><p style="text-align: justify;"><span style="font-size: medium;">3. Jika mencentang kotak cekbox <i><b>Allow selecting multiple choices</b></i>, maka kita akan membuat soal dengan jawaban pilihan benar lebih dari satu.</span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Centang kotak cekbox Has correct answer(s) untuk membuat kunci jawaban, centang satu kotak A, B, C, D atau E yang merupakan kunci jawaban dari soal jika <b>tidak </b></span><span style="font-size: medium;"><span><b>mencentang</b> kotak cekbox </span><span><b style="font-style: italic;">Allow selecting multiple choices </b>dan centang kotak lebih dari satu (1) jika </span><span><b>mencentang</b> kotak cekbox </span><span><b style="font-style: italic;">Allow selecting multiple choices.</b></span></span></p><p style="text-align: justify;"><span style="font-size: medium;">5. Centak kotak cekbox <b><i>Competetion Mode</i></b> jika soal ini ingin dibuat menjadi soal kompetisi.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><b><i><span style="font-size: medium;">Play Option</span></i></b></p><p style="text-align: justify;"><span style="font-size: medium;">1. Centang cekbox <b><i>Start question with slide</i></b> jika ingin menjalankan kuis secara otomatis ketika slide soal di slide show. Jika tidak dicentang soal akan dijalankan jika kita mengklik tombol Multiple choice yang ada di halaman slide setelah di slide show.</span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Centang cekbox <b><i>Minimize result window after question starts</i></b> jika ingin meminimize jendela hasil setelah pertanyaan dimulai</span></p><p style="text-align: justify;"><span style="font-size: medium;">3. Centang cekbox <b><i>Close submission after</i></b> dan pilih waktunya, jika kita ingin mengakhiri ujian pada nomor soal tersebut sesuai dengan waktu pengerjaan soal yang dipilih.</span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Tombol <b>View Responses</b> untuk melihat respon siswa pada soal tersebut setelah selesai ujian dan pada kondisi slide tidak dalam mode slide show.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><h4 style="text-align: justify;"><span style="font-size: medium;">B. Membuat Soal Curah Pendapat dengan Word Cloud</span></h4><p style="text-align: justify;"><span style="font-size: medium;">Fungsi dari Word Cloud adalah sebagai alat visual untuk mengumpulkan pendapat atau pengetahuan siswa atau dalam istilah lain tipe soal ini dapat digunakan untuk kegiatan <b><i>brainstorming</i></b> (curah pendapat untuk mengumpulkan gagasan atau ide untuk mencari solusi dari masalah tertentu).</span></p><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah menggunakan Word Cloud</span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Buatlah pertanyaan curah pendapat di Slide Power Point, misal seperti gambar berikut.</span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAl1FXDg_Vw6WPDRPJ88qlh03I7Hufvxdo82StXEHi6s_qzAG22FG21F81pDG775--SGBEJzYIrAZ-Qgk_22usxXsqSu6nRCAbQQnnicDpGnymWJGO_RDEEtBZT8uPN5wlILBUCVF3hvFB9v52C7NaPxELA4frg72CmcVqkVBVQ2RFCjxqjrkZ_UBu/s400/pemanfaatan6.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Soal Word Cloud" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAl1FXDg_Vw6WPDRPJ88qlh03I7Hufvxdo82StXEHi6s_qzAG22FG21F81pDG775--SGBEJzYIrAZ-Qgk_22usxXsqSu6nRCAbQQnnicDpGnymWJGO_RDEEtBZT8uPN5wlILBUCVF3hvFB9v52C7NaPxELA4frg72CmcVqkVBVQ2RFCjxqjrkZ_UBu/s16000/pemanfaatan6.png" title="Membuat Soal Word Cloud" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Membuat Soal Word Cloud</td></tr></tbody></table><br /><span style="font-size: medium;">2. Klik menu <b>Inknoe ClassPoint</b> dan klik tollbar <b>Word Cloud</b>. Lakukan pengaturan-pengaturan yang dibutuhkan, seperti pada gambar berikut.</span><p></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn3whHSH1jm_ztX2T-0Kd30guLDbF2pmTJ6pUr0_qpxY_l5HCS41JFWM2cP6ikx9vwCnuiqJGZgVCDAfx-w-9SlplB1XN2zQc2So28lJxzxwQnG68rAqEZzvWXaXysmZDbdffsYqLnqDtxiUlxpW5gW2JdexoecSzmLLB5gWV8COdFPL6CMsB0mViF/s400/pemanfaatan7.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Soal Kuis Interaktif Word Cloud" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn3whHSH1jm_ztX2T-0Kd30guLDbF2pmTJ6pUr0_qpxY_l5HCS41JFWM2cP6ikx9vwCnuiqJGZgVCDAfx-w-9SlplB1XN2zQc2So28lJxzxwQnG68rAqEZzvWXaXysmZDbdffsYqLnqDtxiUlxpW5gW2JdexoecSzmLLB5gWV8COdFPL6CMsB0mViF/s16000/pemanfaatan7.png" title="Membuat Soal Kuis Interaktif Word Cloud" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Setting Soal Tipe Word Cloud</td></tr></tbody></table><br /><span style="font-size: medium;"><b><i>Keterangan gambar :</i></b></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Pada kotak <b>Interactive Quiz</b> :</span></p><p style="text-align: justify;"><b><i><span style="font-size: medium;">Question Type</span></i></b></p><p style="text-align: justify;"><span style="font-size: medium;">1. Pada kotak Drop Down tertulis <i><b>Word Cloud</b></i> menunjukkan kita mau membuat soal tipe Word Cloud</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Centang kotak cekbox : <b><i>Limit number submission to</i></b>, lalu klik angka yang diinginkan. Maksudnya kita dapat membatasi jawaban siswa, jika kita pilih angka 1, maka siswa bisa kirim jawaban hanya sekali.</span></p><p style="text-align: left;"><span style="font-size: medium;">Untuk penjelasan <b><i>Play Option</i></b> sama dengan penjelasan pada bagian multiple choice diatas.</span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><h4 style="text-align: justify;"><span style="font-size: medium;">C. Membuat Soal dengan Jawaban Singkat (Short Answer)</span></h4><p style="text-align: justify;"><span style="font-size: medium;">Soal dengan jawaban singkat (Short Answer) memungkinkan siswa untuk mengirimkan jawaban sepanjang 1500 karakter.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah membuat soal dengan Jawaban Singkat (Short Answer)</span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Buatlah soal uraian dengan jawaban singkat pada slide power point, misal seperti gambar berikut.</span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIim7QC50d_aHFi86ghhvk5-tvPCCenKQFlC6Un4LpMhes9G7C3MpZKElNdiIEn-_12n60tyILrmD2-FONxwDzTK7_TWdJEO8VLspyPEg_OZzmAOJ4txcR9ElOCZQmMtV-mnj6f6aA0qlReAcAbiki5bqT5l2XvyUzNVSTww_HFpX6p6j7g1K_fMO7/s400/pemanfaatan8.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat soal uraian di Power Point" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIim7QC50d_aHFi86ghhvk5-tvPCCenKQFlC6Un4LpMhes9G7C3MpZKElNdiIEn-_12n60tyILrmD2-FONxwDzTK7_TWdJEO8VLspyPEg_OZzmAOJ4txcR9ElOCZQmMtV-mnj6f6aA0qlReAcAbiki5bqT5l2XvyUzNVSTww_HFpX6p6j7g1K_fMO7/s16000/pemanfaatan8.png" title="Membuat soal uraian di Power Point" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Membuat soal uraian di Power Point</td></tr></tbody></table><br /><span style="font-size: medium;"><span>2. </span><span>Klik menu <b>Inknoe ClassPoint</b> dan klik tollbar <b>Short Answer</b>. Lakukan pengaturan-pengaturan yang dibutuhkan, seperti pada gambar berikut.</span></span><p></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsaX66KY_pmASRV1exbCWCM0-EGfHhABs5r1UR67MbVJ8fDKDqWT7phCyAbkx6ocOvGid69v0G2UJXqWQvB73lqP5h372vYzs3Nmay9L9QXlGQ5PhaeArxdO9N-rLlC0JyxgtMz6m2UtnipQp04iiE8hNMvrUwmFq1KvMFO3PqlMz0dPNsDGMNYzL_/s400/pemanfaatan9.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Soal Short Answer" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsaX66KY_pmASRV1exbCWCM0-EGfHhABs5r1UR67MbVJ8fDKDqWT7phCyAbkx6ocOvGid69v0G2UJXqWQvB73lqP5h372vYzs3Nmay9L9QXlGQ5PhaeArxdO9N-rLlC0JyxgtMz6m2UtnipQp04iiE8hNMvrUwmFq1KvMFO3PqlMz0dPNsDGMNYzL_/s16000/pemanfaatan9.png" title="Membuat Soal Short Answer" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Setting Soal Short Answer</td></tr></tbody></table><br /><span style="font-size: medium;"><b><i>Keterangan gambar :</i></b></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Pada kotak <b>Interactive Quiz</b> :</span></p><p style="text-align: justify;"><b><i><span style="font-size: medium;">Question Type</span></i></b></p><p style="text-align: justify;"><span style="font-size: medium;">1. Pada kotak Drop Down tertulis <b><i>Short Answer</i></b> menunjukkan kita mau membuat soal tipe Short Answer</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Centang kotak cekbox : <b><i>Hide participant names when viewing respons</i></b>, jika ingin menyembunyikan nama siswa di halaman view Responses.</span></p><p><span style="font-size: medium;">Untuk penjelasan <b><i>Play Option</i></b> sama dengan penjelasan pada bagian multiple choice diatas.</span></p><p><span style="font-size: medium;"><br /></span></p><h4 style="text-align: left;"><span style="font-size: medium;">D. Membuat soal Slide Drawing</span></h4><p style="text-align: justify;"><span style="font-size: medium;">Pada tipe soal ini guru mengirimkan slide kepada siswa untuk diberi anotasi dan dikirim kembali kepada guru.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah membuat soal tipe Slide Drawing</span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Buatkan soal yang membutuhkan penggunaan drawing pada slide power point, misal seperti gambar berikut.</span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNrZCDuQz0B5YI1ma1_CSEi0E6g7U_re5ClbTnCse7g65RzG357yCOs8pDSV3VtV523qbSf6cqEq4ru9RfCrtjQW8Pl55Zsam3jSIAGV1p9GPOl85GAEIm1kjoVrNR7REYIfreO6fk1xBnzjSagQRXWdt-j6ArOEaNC0HB3EH64N5216PnLmAyoNM4/s400/pemanfaatan10.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat soal yang membutuhkan gambar di power point" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNrZCDuQz0B5YI1ma1_CSEi0E6g7U_re5ClbTnCse7g65RzG357yCOs8pDSV3VtV523qbSf6cqEq4ru9RfCrtjQW8Pl55Zsam3jSIAGV1p9GPOl85GAEIm1kjoVrNR7REYIfreO6fk1xBnzjSagQRXWdt-j6ArOEaNC0HB3EH64N5216PnLmAyoNM4/s16000/pemanfaatan10.png" title="Membuat soal yang membutuhkan gambar di power point" /></a></p></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Membuat soal yang membutuhkan gambar di power point</td></tr></tbody></table><br /><span style="font-size: medium;"><span>2. </span><span>Klik menu</span><span> </span><b>Inknoe ClassPoint</b><span> </span><span>dan klik tollbar</span><span> <b>Slide Drawing</b></span><span>. Lakukan pengaturan-pengaturan yang dibutuhkan, seperti pada gambar berikut.</span></span><p></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK3D6SlOO21AdoR1Hm1F9QeWFELLuZFCxk8dMmmDXJgXASBxext-_hXy7V71d4p9q9IKAmeXmOg76z9tAj1qlmr3Rk4KNbJJoAW5h1-TGti0DCzv7X5uBdRauHWErNLRcnHVNgQtY-u4ifhWIs_Av7AcnWfkj1DnZocpybvD35HGb7yyUXbSiVxJq9/s400/pemanfaatan11.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Soal Tipe Slide Drawing" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK3D6SlOO21AdoR1Hm1F9QeWFELLuZFCxk8dMmmDXJgXASBxext-_hXy7V71d4p9q9IKAmeXmOg76z9tAj1qlmr3Rk4KNbJJoAW5h1-TGti0DCzv7X5uBdRauHWErNLRcnHVNgQtY-u4ifhWIs_Av7AcnWfkj1DnZocpybvD35HGb7yyUXbSiVxJq9/s16000/pemanfaatan11.png" title="Membuat Soal Tipe Slide Drawing" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 11. Setting Soal Tipe Slide Drawing</td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-size: medium;"><b><i>Keterangan gambar :</i></b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Pada kotak <b>Interactive Quiz</b> :</span></p><p style="text-align: justify;"><b><i><span style="font-size: medium;">Question Type</span></i></b></p><p style="text-align: justify;"><span style="font-size: medium;">1. Pada kotak Drop Down tertulis <b><i>Slide Drawing</i></b> menunjukkan kita mau membuat soal tipe Slide Drawing</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Centang kotak cekbox : <b><i>Hide participant names when viewing respons</i></b>, jika ingin menyembunyikan nama siswa di halaman view Responses.</span></p><p><span style="font-size: medium;">Untuk penjelasan <b><i>Play Option</i></b> sama dengan penjelasan pada bagian multiple choice diatas.</span></p><p><span style="font-size: medium;"><br /></span></p><h4 style="text-align: left;"><span style="font-size: medium;">E. Membuat Soal tipe Image upload</span></h4><p><span style="font-size: medium;">Pada tipe soal ini siswa dapat mengunggah gambar sebagai jawaban.</span></p><p><span style="font-size: medium;">Langkah-langkah membuat soal tipe Image Upload</span></p><p><span style="font-size: medium;">1. Buatlah soal yang membutuhkan jawaban dalam bentuk gambar di Power Point, Misal seperti gambar berikut.</span></p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHZR5gn5ilV238fUaPktQ_iZqpgOK1UnWATPSz2ryK00mD8hQIG3Cnb6QhCp2TLLO48hjxOfvLJDbkJsv25u7yi6yqnuL1q8NGQGSlwGt1o9lKdsu9wla40Yg73pJ3Zo61tHFF4em62zIkYxxC-qeDW3aOr8QiqX57v2-FANvIUEqdurgloMNo-Ggf/s400/Pemanfaatan12.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat soal yang membutuhkan jawaban gambar" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHZR5gn5ilV238fUaPktQ_iZqpgOK1UnWATPSz2ryK00mD8hQIG3Cnb6QhCp2TLLO48hjxOfvLJDbkJsv25u7yi6yqnuL1q8NGQGSlwGt1o9lKdsu9wla40Yg73pJ3Zo61tHFF4em62zIkYxxC-qeDW3aOr8QiqX57v2-FANvIUEqdurgloMNo-Ggf/s16000/Pemanfaatan12.png" title="Membuat soal yang membutuhkan jawaban gambar" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 12. Membuat soal yang membutuhkan jawaban gambar</td></tr></tbody></table><br /><p style="text-align: justify;"><span style="font-size: medium;"><span>2. </span><span style="text-align: justify;">Klik menu</span><span style="text-align: justify;"> </span><b style="text-align: justify;">Inknoe ClassPoint</b><span style="text-align: justify;"> </span><span style="text-align: justify;">dan klik tollbar</span><span style="text-align: justify;"> <b>Image Upload</b></span><span style="text-align: justify;">. Lakukan pengaturan-pengaturan yang dibutuhkan, seperti pada gambar berikut.</span></span></p><p></p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw2IC8YxS-cKaIamO1MYItTIvYnlH5S_7z5n6cWLolcxmDGIUkWbCpC36dhpQj-vbTw-SQkaWpt4NpEtZeePPYQimsk8zglSeWg7888gO1DjEoOcFwzVOuEvFRgrVcNu91mXERq4tNedStoGl1hqzLcrlwZT-_F6IR9nVXSrtHWyHs1sO8EACk8-kH/s400/pemnafaatan13.png" style="margin-left: auto; margin-right: auto;"><img alt="Setting Soal Tipe Image Upload" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw2IC8YxS-cKaIamO1MYItTIvYnlH5S_7z5n6cWLolcxmDGIUkWbCpC36dhpQj-vbTw-SQkaWpt4NpEtZeePPYQimsk8zglSeWg7888gO1DjEoOcFwzVOuEvFRgrVcNu91mXERq4tNedStoGl1hqzLcrlwZT-_F6IR9nVXSrtHWyHs1sO8EACk8-kH/s16000/pemnafaatan13.png" title="Setting Soal Tipe Image Upload" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 13. Setting Soal Tipe Image Upload</td></tr></tbody></table><br /><span style="font-size: medium; text-align: justify;"><b><i>Keterangan Gambar</i></b></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Pada kotak <b>Interactive Quiz</b> :</span></p><p style="text-align: justify;"><b><i><span style="font-size: medium;">Question Type</span></i></b></p><p style="text-align: justify;"><span style="font-size: medium;">1. Pada kotak Drop Down tertulis <b><i>Image Upload</i></b> menunjukkan kita mau membuat soal tipe Image Upload.</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Centang kotak cekbox : <b><i>Hide participant names when viewing respons</i></b>, jika ingin menyembunyikan nama siswa di halaman view Responses.</span></p><p><span style="font-size: medium;">Untuk penjelasan <b><i>Play Option</i></b> sama dengan penjelasan pada bagian multiple choice diatas.</span></p><p><span style="font-size: medium;">Demikian Cara Membuat Soal interaktif di ClassPoint. Selanjutnya akan dibahas Penerapan ClassPoint pada pembelajaran interaktif.</span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-70563408867581424712022-11-20T18:10:00.003+08:002022-11-29T12:50:18.481+08:00Langkah-langkah Install ClassPoint<p style="text-align: justify;"><span style="font-size: medium;"><b>Langkah-langkah Install ClassPoint -</b> Sebelum melakukan instalasi aplikasi ClassPoint ini, yang perlu perhatikan adalah sistem ini kompatibel dengan :</span></p><p></p><ul style="text-align: left;"><li><span style="font-size: medium;">Windows 10/11</span></li><li><span style="font-size: medium;">Office 2013/2016/2019/2021/365</span></li></ul><p style="text-align: justify;"><span style="font-size: medium;">Setelah persyaratan sistem diatas terpenuhi, kita bisa melakukan instalasi dengan langkah-langkah sebagai berikut.</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">LANGKAH-LANGKAH INSTALL CLASSPOINT</span></h3><p style="text-align: justify;"><span style="font-size: medium;">1. Dari browser anda ketik "classpoint" pada kotak pencarian dan klik Classpoint: Interactive seperti gambar dibawah klik link <a href="https://www.classpoint.io/" rel="nofollow" target="_blank">https://www.classpoint.io/</a> seperti gambar berikut</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHwAtrRJVhW43-Tf5Udj-Apc5YJ4Eo9rIMqZKhGzRP6oplOlK9boSKmCtD1r5wOhEivw1tgYrza7vMtmEoT_8mqgGbPoARpnsTYGEG-VAlzEy-pDOt145Qr4gKmYH7YGCgOJcJOdGNiKfTzv3pgDg4bR8HtVuo-8yaoEHhgt_vMOvMHPA0S8XbtQb3/s400/GAMBAR%201-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Pencarian ClassPoint di browser" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHwAtrRJVhW43-Tf5Udj-Apc5YJ4Eo9rIMqZKhGzRP6oplOlK9boSKmCtD1r5wOhEivw1tgYrza7vMtmEoT_8mqgGbPoARpnsTYGEG-VAlzEy-pDOt145Qr4gKmYH7YGCgOJcJOdGNiKfTzv3pgDg4bR8HtVuo-8yaoEHhgt_vMOvMHPA0S8XbtQb3/s16000/GAMBAR%201-1.png" title="Pencarian ClassPoint di browser" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><p>Gambar 1 : Mencari ClassPoint Melalui Browser</p></td></tr></tbody></table><span style="font-size: medium;"><br /></span><p style="text-align: justify;"><span style="font-size: medium;">2. Selanjutnya akan diarahkan ke halaman awal classpoint. Dari halaman tersebut klik tombol <b>FREE DOWNLOAD</b>, seperti gambar berikut.</span></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiONvgOW2rdSNUxRxMlRP0qq4VDaaYZLgAbqw6I8y2E20O1lpjscE28esFBwjGRoMuSMNvQVwG_aiCvWCX3HgR7_AO6xsRjsdMaxKdJrwOXUrqoaYHhdhFwsrjC2S4d7_5x-x985ufg17SgShuhHMmqZ3veGWJK56Z4ydNjsjxsXJnICbvGq9RS8kxa/s400/GAMBAR%202-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Halaman download classpoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiONvgOW2rdSNUxRxMlRP0qq4VDaaYZLgAbqw6I8y2E20O1lpjscE28esFBwjGRoMuSMNvQVwG_aiCvWCX3HgR7_AO6xsRjsdMaxKdJrwOXUrqoaYHhdhFwsrjC2S4d7_5x-x985ufg17SgShuhHMmqZ3veGWJK56Z4ydNjsjxsXJnICbvGq9RS8kxa/s16000/GAMBAR%202-1.png" title="Halaman download classpoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Halaman Download ClassPoint</td></tr></tbody></table><p></p><span style="font-size: medium;"><br /></span><p style="text-align: justify;"><span style="font-size: medium;">3. Setelah itu pada halaman download, isilah kotak Your Name (Masukkan nama anda), Your Email (gunakan email aktif, misal "namaemail@gmail.com" dan Organization (Ketik nama organisasi anda). Setelah itu klik tombol <b>DOWNLOAD NOW</b>, seperti pada gambar berikut.</span></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglxz74RWyXhasl6yWcTNqzRHLNe6CH8Gtuajjcj6Gf4n27Q7jQilqJVTedhYxaTTmJAoYxATn0wLIgjMQ6gYUhrsOChHEIQ-5fWG4tP3uL3Msf3hUx57_xi_8x6IcMTa5gGqworLYF0sr17xJElw6bFKdyhcb-EqkbSGIUKc4UBSVHJyZzhI9mC-nt/s400/GAMBAR%203-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Isian identitas user sebelum mendownload" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglxz74RWyXhasl6yWcTNqzRHLNe6CH8Gtuajjcj6Gf4n27Q7jQilqJVTedhYxaTTmJAoYxATn0wLIgjMQ6gYUhrsOChHEIQ-5fWG4tP3uL3Msf3hUx57_xi_8x6IcMTa5gGqworLYF0sr17xJElw6bFKdyhcb-EqkbSGIUKc4UBSVHJyZzhI9mC-nt/s16000/GAMBAR%203-1.png" title="Isian identitas user sebelum mendownload" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Isian identitas user sebelum mendownload</td></tr></tbody></table><p></p><span style="font-size: medium;"><br /></span><p style="text-align: justify;"><span style="font-size: medium;">4. Tunggu proses download berhasil klik open file atau jika tidak muncul cari file downloadnya di windows explorer dan jalankan file tersebut. seperti pada gambar berikut.</span></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9cDWa0WGpmw7VCDvN6YYPiQns2NoqWczJRghF0uHJ_GW2RnET9qvy2L_ATqb9AIfvLfeAReii6P_CU6QLeHGqfwbjy8u8jv0QlRXZSftxAnb2s8lpFcvhZ7RqBjubC333LwW0d_qhkp4PR8im0Za3d1w97dMBKHpfIuz6P5ODUyNqaFmY1ffpl1SI/s400/GAMBAR%205-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Hasil download file aplikasi classpoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9cDWa0WGpmw7VCDvN6YYPiQns2NoqWczJRghF0uHJ_GW2RnET9qvy2L_ATqb9AIfvLfeAReii6P_CU6QLeHGqfwbjy8u8jv0QlRXZSftxAnb2s8lpFcvhZ7RqBjubC333LwW0d_qhkp4PR8im0Za3d1w97dMBKHpfIuz6P5ODUyNqaFmY1ffpl1SI/s16000/GAMBAR%205-1.png" title="Hasil download file aplikasi classpoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Hasil download file aplikasi classpoint</td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">5. Setelah itu akan muncul kotak Inknoe ClassPoint Setup, centang kotak cekbox <i><b>I accept Inknoe's license term and condition</b></i>, lalu klik tombol <b>Install</b>. Seperti gambar berikut</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSrOgwcjJ6UbvlPPxSFM9To0xtPZfC_9Yrr54Ln5BVb0XNem7ZFSXpOT_gKOaEDtxCvwJTXGB_n6fTLon4tmr0Ho3aDjE3NARdv6gsds9GEkWMyj6Nw42gMr-IMohfgmAHvmwnkvX83Ayg-ImsScVQoh0fk80nvAZgkDr_fwdUPhq70EmO_npPadtg/s400/GAMBAR%206-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Kotak Inknoe ClassPoint Setup" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSrOgwcjJ6UbvlPPxSFM9To0xtPZfC_9Yrr54Ln5BVb0XNem7ZFSXpOT_gKOaEDtxCvwJTXGB_n6fTLon4tmr0Ho3aDjE3NARdv6gsds9GEkWMyj6Nw42gMr-IMohfgmAHvmwnkvX83Ayg-ImsScVQoh0fk80nvAZgkDr_fwdUPhq70EmO_npPadtg/s16000/GAMBAR%206-1.png" title="Kotak Inknoe ClassPoint Setup" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Kotak Inknoe ClassPoint Setup</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p style="text-align: justify;"><span style="font-size: medium;">6. Tunggu proses persiapan instalasi selesai, akan muncul seperti pada gambar berikut.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir7vphbwG4QVofJxyT6E2T2pXQ00LrzvSiD5b5YwkzUF4BRttqKqRtWdI8xBfz4Y-TTSFfJ99m5GlRgHLq8kSWI1hx_rJewOJ3CmiZELX6d0EU1ALiskWPDhlM8mdHle3_1WS5L_YO20QEEoeIcvlGF3j4li7nCK0v1nKWDHQvJwM7MlsBESqbyOTL/s400/GAMBAR%207-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Persiapan Instalasi Aplikasi ClassPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir7vphbwG4QVofJxyT6E2T2pXQ00LrzvSiD5b5YwkzUF4BRttqKqRtWdI8xBfz4Y-TTSFfJ99m5GlRgHLq8kSWI1hx_rJewOJ3CmiZELX6d0EU1ALiskWPDhlM8mdHle3_1WS5L_YO20QEEoeIcvlGF3j4li7nCK0v1nKWDHQvJwM7MlsBESqbyOTL/s16000/GAMBAR%207-1.png" title="Persiapan Instalasi Aplikasi ClassPoint" /></span></a></p></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Persiapan Instalasi Aplikasi ClassPoint</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p style="text-align: justify;"><span style="font-size: medium;">7. Setelah itu akan muncul kotak Wellcome to Microsoft Visual Studio Tool For Office Runtime 2010 Setup. Centang cekbox <i><b>I have read and accept the license terms</b></i>. Lalu klik tombol <b>Install</b>. seperti gambar berikut</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn84vGfXteMv94WInTFwWhI-V_aoLeRtIT6KKnXvtnHVyjZU3fB6ks5PH8v25MQ0XrK8xpx87hBj_MF-mG9flohQ7ZtshQRUA16WS25JADZXIAIyb3yxagb1628GgDduJ6MO-Fq2FIarWWxy7RPPtrcDrgNi4WLsJFQJxktGQEWh-sOEo8kC8i8sCH/s400/GAMBAR%207-2.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="kotak Wellcome to Microsoft Visual Studio Tool For Office Runtime 2010 Setup" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn84vGfXteMv94WInTFwWhI-V_aoLeRtIT6KKnXvtnHVyjZU3fB6ks5PH8v25MQ0XrK8xpx87hBj_MF-mG9flohQ7ZtshQRUA16WS25JADZXIAIyb3yxagb1628GgDduJ6MO-Fq2FIarWWxy7RPPtrcDrgNi4WLsJFQJxktGQEWh-sOEo8kC8i8sCH/s16000/GAMBAR%207-2.png" title="kotak Wellcome to Microsoft Visual Studio Tool For Office Runtime 2010 Setup" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Wellcome to Microsoft Visual Studio Tool For Office Runtime 2010 Setup</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p style="text-align: justify;"><span style="font-size: medium;">8. Proses instalasi aplikasi <span style="text-align: center;">Microsoft Visual Studio Tool For Office Runtime 2010</span> sedang berjalan tunggu sampai proses selesai, seperti gambar berikut.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC52oHy8mJlwoDC2Fn9cwcogbReI3EJDIfVZHqGs16Bi-R1U_tK8cnJZioqpCNEGCEVKjxV-_PT2-cFPau5KDvpQkaK286S8JzluKESODgL7HaiK3xR-5wVi0T8an6Zkya2PYA7-DDNWgU9L6RAXkY1rDzD1FBEy9uFGoWP_kvHjEidBLtMxtHI32F/s400/GAMBAR%208-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Proses Install ClassPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC52oHy8mJlwoDC2Fn9cwcogbReI3EJDIfVZHqGs16Bi-R1U_tK8cnJZioqpCNEGCEVKjxV-_PT2-cFPau5KDvpQkaK286S8JzluKESODgL7HaiK3xR-5wVi0T8an6Zkya2PYA7-DDNWgU9L6RAXkY1rDzD1FBEy9uFGoWP_kvHjEidBLtMxtHI32F/s16000/GAMBAR%208-1.png" title="Proses Install ClassPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Proses Install Microsoft Visual Studio Tool For Office Runtime 2010</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p style="text-align: justify;"><span style="font-size: medium;">9. Jika install <span style="text-align: center;">Microsoft Visual Studio Tool For Office Runtime 2010 sudah selesai akan muncul kotak seperti ini, klik tombol <b>Finish</b>, seperti gambar berikut.</span></span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0pzuhWf1LbFwUdVssT9x2oNHO-NbysUVzSQFJK9ObOEWIDND41UpwRL3kZJQtp8yr4865aN8rU8Hll30PRsHmJYk3RuYAF3PT3PX3RJ2AH86rIWp3JNcwahb4g-aSrsTzjDXqNkxxidXTc5pEtjR8HCdFtcfxykpE4-wIkKSYZj_v03MK_9IsHRTH/s400/GAMBAR%209-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Install Microsoft Visual Studio Tool For Office Runtime 2010 sukses" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0pzuhWf1LbFwUdVssT9x2oNHO-NbysUVzSQFJK9ObOEWIDND41UpwRL3kZJQtp8yr4865aN8rU8Hll30PRsHmJYk3RuYAF3PT3PX3RJ2AH86rIWp3JNcwahb4g-aSrsTzjDXqNkxxidXTc5pEtjR8HCdFtcfxykpE4-wIkKSYZj_v03MK_9IsHRTH/s16000/GAMBAR%209-1.png" title="Install Microsoft Visual Studio Tool For Office Runtime 2010 sukses" /></span></a></p></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Install Microsoft Visual Studio Tool For Office Runtime 2010 sukses</td></tr></tbody></table><span style="font-size: medium;"><br /><span style="text-align: center;">10. Selanjutnya akan muncul kotak Inknoe ClassPoint Setup untuk memulai install aplikasi ClassPoint. Klik tombol <b>Next</b>, seperti gambar berikut.</span></span><p></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8SQ88Vhury5NNl-noRklqZLS5LrMcjmiZxcuDLfeB05vfHlJb-sw0AVWQCweeFUc_ZCWtb6SHpZtI9B9uWVGb6FS-ZplgEu5vJwgcHNG4FAWhdD3As9HP4P8cV6_oK0T-Rk5CLTbQkLLbEzfXyAudCHBzbyrgJXrylbkvTYOALHz1sqK_y4i__X6y/s400/GAMBAR%2010-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Memulai Install ClassPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8SQ88Vhury5NNl-noRklqZLS5LrMcjmiZxcuDLfeB05vfHlJb-sw0AVWQCweeFUc_ZCWtb6SHpZtI9B9uWVGb6FS-ZplgEu5vJwgcHNG4FAWhdD3As9HP4P8cV6_oK0T-Rk5CLTbQkLLbEzfXyAudCHBzbyrgJXrylbkvTYOALHz1sqK_y4i__X6y/s16000/GAMBAR%2010-1.png" title="Memulai Install ClassPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Memulai Install ClassPoint</td></tr></tbody></table><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><span style="font-size: medium;"><span style="text-align: center;">11. Tunggu proses Instalasi ClassPoint sedang berjalan, seperti gambar berikut</span></span><p></p><p style="text-align: justify;"></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_1LskZdeUK6KWP5BN-nePD6kaQe-vEozK5NQ-tcl_A5aQhal5Vxz3Qp2_TWbZl6ZBE6IzCwDbPUcb3dcTXSPRxR3pCJ3GRIH0ZrHW3SgE4ozxDDgfEpZeyVhOQLzBpsQAubyEqwWhN0y7NiXaaZJ_bWzk1SKE3OberPEFEJSq2Yvn8Q2TEG_qaghF/s400/GAMBAR%2011-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Proses Install ClassPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_1LskZdeUK6KWP5BN-nePD6kaQe-vEozK5NQ-tcl_A5aQhal5Vxz3Qp2_TWbZl6ZBE6IzCwDbPUcb3dcTXSPRxR3pCJ3GRIH0ZrHW3SgE4ozxDDgfEpZeyVhOQLzBpsQAubyEqwWhN0y7NiXaaZJ_bWzk1SKE3OberPEFEJSq2Yvn8Q2TEG_qaghF/s16000/GAMBAR%2011-1.png" title="Proses Install ClassPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 11. Proses Install ClassPoint</td></tr></tbody></table><p></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium; text-align: center;">12. Jika instalasi selesai dan sukses akan tampak kotak Inknoe ClassPoint Setup seperti ini. Klik tombol <b>Finish</b>.</span></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho1OogoTJOwkD1DAK1V6jI6BOuSQT1RJFK8oEeXjl56It21qrwENzMO_rbCMzzQAVVS3smDkMihFP31nHdlwk2j3H7J2q7Y-fvkZlMQvStgknDApoRNRB_69uoNvqxInYmyasJNoSAXrP0hXqMG35E-tMM9EIaffTKppGIKFS2gVeQyb7qXUGqVdMW/s400/GAMBAR%2012-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Instalasi ClassPoint Berhasil" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho1OogoTJOwkD1DAK1V6jI6BOuSQT1RJFK8oEeXjl56It21qrwENzMO_rbCMzzQAVVS3smDkMihFP31nHdlwk2j3H7J2q7Y-fvkZlMQvStgknDApoRNRB_69uoNvqxInYmyasJNoSAXrP0hXqMG35E-tMM9EIaffTKppGIKFS2gVeQyb7qXUGqVdMW/s16000/GAMBAR%2012-1.png" title="Instalasi ClassPoint Berhasil" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 12. Install ClassPoint Berhasil</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">13. Setelah itu akan dilakukan proses Updating Classpoint. Tunggu proses ini selesai. Tampak seperti gambar berikut.</span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC5CH5Caff1zMetS5hlNrVtnYiPWNkn-XN27NmSkUDvbEpF9o5OaEePVAdIDyn6VGtStR1h0h751jIj3ZRaXcFaXv8sxg1DEfRKgtfCtawNvbzltmtePXwhUafZcdmd3pr3WwYGbzqinFMbn8SJhO3JIBQwbajrS75n6YHLPBsdtlv3Ybsi54wGA-D/s400/GAMBAR%2013-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Updating ClassPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC5CH5Caff1zMetS5hlNrVtnYiPWNkn-XN27NmSkUDvbEpF9o5OaEePVAdIDyn6VGtStR1h0h751jIj3ZRaXcFaXv8sxg1DEfRKgtfCtawNvbzltmtePXwhUafZcdmd3pr3WwYGbzqinFMbn8SJhO3JIBQwbajrS75n6YHLPBsdtlv3Ybsi54wGA-D/s16000/GAMBAR%2013-1.png" title="Updating ClassPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><p>Gambar 13. Updating ClassPoint</p></td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">14. Setelah itu Klik tombol </span><b style="text-align: center;">Open PowerPoint</b><span style="text-align: center;">. Seperti tampak pada gambar berikut</span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6rKJW8c1lipRaI0vN-BZQoW680XcveZd7Z5jccvb4aMsEPMXotC4wvwR3Wh546hwKZ6Q_-URYRoxxazSOpMhA4fOcfTnAO_SGeRvOeyYI3TKyd_TTZbDMao00XmaKcnH6-iNf9zezEnvf2xLk3-dXzbxT8m8fTNIAcaw7Jvy9ZXVwsYwph9wacmQA/s400/GAMBAR%2014-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Open PowerPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6rKJW8c1lipRaI0vN-BZQoW680XcveZd7Z5jccvb4aMsEPMXotC4wvwR3Wh546hwKZ6Q_-URYRoxxazSOpMhA4fOcfTnAO_SGeRvOeyYI3TKyd_TTZbDMao00XmaKcnH6-iNf9zezEnvf2xLk3-dXzbxT8m8fTNIAcaw7Jvy9ZXVwsYwph9wacmQA/s16000/GAMBAR%2014-1.png" title="Open PowerPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 14. Open PowerPoint</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">15. Akan tampak halaman Welcome to ClassPoint.pptx di aplikasi Power Point seperti gambar baerikut</span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMg5BcTbdjuz9S4nuMo9PRH0tDkCpR4T6XHzh9SrbFMkpJjevtyOvrfKKdtueRRL0t2nGHQLyfRiLMW9fC1RUvsSWpDRTwe0I-yQfNn51sO_GQn7_-cMcfLy7agqjY40d5Y-OjV4Brdhl3Ox9U84BYkZfZZHky2RRotIDPhDlUOOvOljjhQJF0vkD1/s400/GAMBAR%2016-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Welcome to ClassPoint.pptx di aplikasi Power Point" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMg5BcTbdjuz9S4nuMo9PRH0tDkCpR4T6XHzh9SrbFMkpJjevtyOvrfKKdtueRRL0t2nGHQLyfRiLMW9fC1RUvsSWpDRTwe0I-yQfNn51sO_GQn7_-cMcfLy7agqjY40d5Y-OjV4Brdhl3Ox9U84BYkZfZZHky2RRotIDPhDlUOOvOljjhQJF0vkD1/s16000/GAMBAR%2016-1.png" title="Welcome to ClassPoint.pptx di aplikasi Power Point" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 15. Welcome to ClassPoint.pptx di aplikasi Power Point</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">16. Klik Tab </span><b style="text-align: center;">Inknoe ClassPoint</b><span style="text-align: center;">, kemudian klik Toll Bar </span><b style="text-align: center;">Sign Up</b><span style="text-align: center;">, seperti pada gambar berikut</span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhX8plqBfjij2b3nSk9ZH8KXfI0fW0D4JS330S_LfP_Mjsr8wnGsvSGopk_DTUEY5E_JHucw4xXkqXEcfiD9FDsBZHxoPspNiGkSFSXK_FPcbe9wCbBL32R1-2Oyc_OV_Ovln_T-dEA1CT65O4ZWPJoXKBcSP1d4Wd1xv0oHlfF-GOZjLzlraTTe8th/s400/GAMBAR%2017-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Sign Up ke ClassPoint" border="0" data-original-height="240" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhX8plqBfjij2b3nSk9ZH8KXfI0fW0D4JS330S_LfP_Mjsr8wnGsvSGopk_DTUEY5E_JHucw4xXkqXEcfiD9FDsBZHxoPspNiGkSFSXK_FPcbe9wCbBL32R1-2Oyc_OV_Ovln_T-dEA1CT65O4ZWPJoXKBcSP1d4Wd1xv0oHlfF-GOZjLzlraTTe8th/s16000/GAMBAR%2017-1.png" title="Sign Up ke ClassPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 16. Sign Up ke ClassPoint</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">17. Pada kotak ClassPoint Sign Up, isilah nama depan, nama belakang, organisasi, sector dan negara, kemudian klik tombol </span><b style="text-align: center;">Next</b><span style="text-align: center;">. Tampak seperti pada gambar berikut</span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJCEs-9uoB5jcTokb5plA5mcVlDLaBo4jToA1bCJ1eOJKvQAWSkqt2Gcvxk3Jdg144sK2EG4u4Ry4ghWiV-bjEF-07BFpmwPKxOSwQS53TNvDrm0T48PzsM4LwHFQ-EkpWdAcBeCBaU70pp6cFIrPKzRsE1Ofz1Z5OujnpXI-o0dJ9rW71L5K4uMji/s400/GAMBAR%2018-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Isian pada kotak ClassPoint Sign Up" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJCEs-9uoB5jcTokb5plA5mcVlDLaBo4jToA1bCJ1eOJKvQAWSkqt2Gcvxk3Jdg144sK2EG4u4Ry4ghWiV-bjEF-07BFpmwPKxOSwQS53TNvDrm0T48PzsM4LwHFQ-EkpWdAcBeCBaU70pp6cFIrPKzRsE1Ofz1Z5OujnpXI-o0dJ9rW71L5K4uMji/s16000/GAMBAR%2018-1.png" title="Isian pada kotak ClassPoint Sign Up" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 17. Isian pada kotak ClassPoint Sign Up</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">18. Setalah itu masukkan email aktif dan buatlah password sesuai dengan keinginan anda kemudian klik tombol </span><b style="text-align: center;">Next</b><span style="text-align: center;">, seperti pada gambar berikut</span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQ_J6UuswbuWNJRkvuBrwSrFMNamdeU6MeEl_5fa4oGz6PSAE12WKdDkNfwr7NwdUgw-budFIa8weFgXlA64QRBlgX1gq5ZovITCyrLVyyL1lkHZy45g7Tvu6qDUddwv0bZYEdeJHemG9glfGbzmlbwABhe8yaG-mxAQs4ZvgpD4xZA-jaXZ1oaAWL/s400/GAMBAR%2019-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Input Email dan Password ClassPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQ_J6UuswbuWNJRkvuBrwSrFMNamdeU6MeEl_5fa4oGz6PSAE12WKdDkNfwr7NwdUgw-budFIa8weFgXlA64QRBlgX1gq5ZovITCyrLVyyL1lkHZy45g7Tvu6qDUddwv0bZYEdeJHemG9glfGbzmlbwABhe8yaG-mxAQs4ZvgpD4xZA-jaXZ1oaAWL/s16000/GAMBAR%2019-1.png" title="Input Email dan Password ClassPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 18. Input Email dan Password ClassPoint</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">19. Setelah itu buka email yang telah anda daftarkan diatas, akan dikirimkan 6 digit kode verifikasi dari ClassPoint registration assistance. Copy kode tersebut dan paste di kotak 6-Digit verification code, kemudian klik tombol <b>Next</b>. Seperti pada gambar berikut</span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS5x7w2jdbKrS_k_uUQwAOl_8AvEtO9nwm8icMTEXH-25ULqhmRiMzZk9stQbNLkxYBaHVmrQ3w_y1bBKYoaX_jn9EbOZHRD6CXZ9qjkSqVrGfR_L4Q8d8x2N-QR5iZEqNz45p4t5UgH-rqJLqL5XZw03iVI9XEPT_ek60j6D1kjPMm2Ff9uHJEP0L/s400/GAMBAR%2020-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Input 6-Digit Verification Code" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS5x7w2jdbKrS_k_uUQwAOl_8AvEtO9nwm8icMTEXH-25ULqhmRiMzZk9stQbNLkxYBaHVmrQ3w_y1bBKYoaX_jn9EbOZHRD6CXZ9qjkSqVrGfR_L4Q8d8x2N-QR5iZEqNz45p4t5UgH-rqJLqL5XZw03iVI9XEPT_ek60j6D1kjPMm2Ff9uHJEP0L/s16000/GAMBAR%2020-1.png" title="Input 6-Digit Verification Code" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 19. Input 6-Digit Verification Code</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">20. Jika input code berhasil akan muncul kotak berikut dan klik tombol <b>Sign In</b></span></span></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibEHdmOnizTr-Ocq-aZkKzk9UGtrU4SJ8crZZa7hfOLO_cL6zQUErj2a21idYE60YviX2N622xFi7eZ6vsi88zc51mY9r_BuD0mbv5FNNy5w2oNMwvor7_NlfPc3lMvx56_3c0A46eI4_d7pewG58W0IQMUS_JRRTEJa4dK6ISTgLFwj_-xyivwGcJ/s400/GAMBAR%2023-1.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Sign In ClassPoint" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibEHdmOnizTr-Ocq-aZkKzk9UGtrU4SJ8crZZa7hfOLO_cL6zQUErj2a21idYE60YviX2N622xFi7eZ6vsi88zc51mY9r_BuD0mbv5FNNy5w2oNMwvor7_NlfPc3lMvx56_3c0A46eI4_d7pewG58W0IQMUS_JRRTEJa4dK6ISTgLFwj_-xyivwGcJ/s16000/GAMBAR%2023-1.png" title="Sign In ClassPoint" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 20. Sign In ClassPoint</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: center;">21. Selamat anda berhasil Install, Sign Up dan Sign In ke ClassPoint. Ingat selalu Email dan Password anda yang telah diinput pada proses sign up diatas. Halaman Aplikasi Power Point sudah terintegrasi dengan aplikasi ClassPoint seperti tampak pada gambar berikut</span><span style="text-align: center;"> </span></span></div><p></p><p style="text-align: left;"><span style="font-size: medium; text-align: center;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuG0AdAu-v59EgzT34G8cCAAYbZoUB9t8JdukYyvjyDpOk1T_zsWIZo2Y3GdIUwTK7b_5emKRXsU7WAKVQJpNbvJj-VHB4QFC9_bI8meB2ym3l0nH-93wFILC267gikh-86VxUvOXUoHl6tkH9yycZKL840t2lZcHACjiFqE77cUkNclkRIk6dM2NM/s682/GAMBAR%2024-1.png" style="margin-left: auto; margin-right: auto;"><img alt="Halaman PowerPoint yang sudah terintegrasi dengan ClassPoint" border="0" data-original-height="383" data-original-width="682" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuG0AdAu-v59EgzT34G8cCAAYbZoUB9t8JdukYyvjyDpOk1T_zsWIZo2Y3GdIUwTK7b_5emKRXsU7WAKVQJpNbvJj-VHB4QFC9_bI8meB2ym3l0nH-93wFILC267gikh-86VxUvOXUoHl6tkH9yycZKL840t2lZcHACjiFqE77cUkNclkRIk6dM2NM/w640-h360/GAMBAR%2024-1.png" title="Halaman PowerPoint yang sudah terintegrasi dengan ClassPoint" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 21. Halaman PowerPoint yang sudah terintegrasi dengan ClassPoint</td></tr></tbody></table><span style="font-size: medium; text-align: center;"><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: center;">Demikan penjelasan tentang langkah-langkah install ClassPoint. Selanjutnya kami akan menjelaskan bagaimana <a href="https://www.sambimatika.my.id/2022/11/cara-membuat-soal-interaktif-di-classpoint.html" target="_blank">cara membuat soal interaktif di ClassPoint untuk pembelajaran</a>. Semoga bermanfaat.</span></p><p></p><p></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-75567388676052138252022-10-29T11:33:00.014+08:002022-11-02T19:40:09.058+08:00Pembahasan Soal-Soal Matriks<p style="text-align: justify;"><span style="font-size: medium;"><b></b></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifdr6U9jc5l0QBDoEMaHZNsJ9bNi0jXSgzkND5hAHPS-yJdbWVywICmfp7oNIMzBfEsKh5oxZFsfaujUyYUsCCNNyBCEg5yMFf4wIo1i3t1ppQz3iTQJC3ZYXuVSDBlIkDIsd3i9UDsvzZJn8sxmM39t4ZptGX762vzxOkI2IpA3xtOvp35iYKg9Cm/s1080/matriks.png" style="margin-left: 1em; margin-right: 1em;"><img alt="Pembahasan Soal Matriks" border="0" data-original-height="1080" data-original-width="1080" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifdr6U9jc5l0QBDoEMaHZNsJ9bNi0jXSgzkND5hAHPS-yJdbWVywICmfp7oNIMzBfEsKh5oxZFsfaujUyYUsCCNNyBCEg5yMFf4wIo1i3t1ppQz3iTQJC3ZYXuVSDBlIkDIsd3i9UDsvzZJn8sxmM39t4ZptGX762vzxOkI2IpA3xtOvp35iYKg9Cm/w200-h200/matriks.png" style="float: left; margin: 5px 9px;" title="Pembahasan Soal Matriks" width="200" /></a></b></span></div><span style="font-size: medium;"><p style="text-align: justify;"><b>Pembahasan Soal-Soal Matriks -</b> Pada beberapa pembahasan sebelumnya sudah dibahas materi tentang matriks, dan pada pembahasan kali ini khusus membahas tentang soal-soal pada matriks yang bisa dijadikan salah satu alternatif untuk belajar bagi yang sedang mempelajari bahasan ini. Soal-soal ini juga sebagian besar pernah keluar di ujian-ujian, seperti UMPTN, SNMPTN, SBMPTN, ujian masuk perguruan tinggi dan ujian lainnya. Tulisan ini diambil dari berbagai sumber diantaranya, soal-soal UMPTN, SBMPTN, Ujian Nasional (UN), Ujian Nasional Berbasis Komputer (ANBK), Ujian Sekolah dan dari buku literatur lainnya. Berikut Pembahasan Soal-Soal Matriks.</p><p style="text-align: justify;"><br /></p><h2 style="text-align: justify;"><span>Soal-Soal Matriks dan Pembahasannya</span></h2><div style="text-align: justify;"><br /></div></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">1. Jika <img src="https://latex.codecogs.com/svg.image?M=\begin{pmatrix}-2&space;&&space;5&space;\\1&space;&&space;-3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?M=\begin{pmatrix}-2 & 5 \\1 & -3 \\\end{pmatrix}" /> dan<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}" /> maka <i>K</i> =....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>A. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}4&space;&&space;3&space;\\-2&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}4 & 3 \\-2 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}1&space;&&space;-2&space;\\3&space;&&space;4&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}1 & -2 \\3 & 4 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1&space;&&space;-2&space;\\3&space;&&space;4&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1 & -2 \\3 & 4 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}3&space;&&space;-4&space;\\1&space;&&space;-2&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}3 & -4 \\1 & -2 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>E. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}1&space;&&space;2&space;\\3&space;&&space;4&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}1 & 2 \\3 & 4 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><span style="text-align: left;"></span>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Cara 1.</b> Menggunakan sifat-sifat perkalian dan kesamaan dua matriks</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}" /> untuk <img src="https://latex.codecogs.com/svg.image?M=\begin{pmatrix}-2&space;&&space;5&space;\\1&space;&&space;-3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?M=\begin{pmatrix}-2 & 5 \\1 & -3 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal <img src="https://latex.codecogs.com/svg.image?K=\begin{pmatrix}a&space;&&space;b&space;\\c&space;&&space;d&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?K=\begin{pmatrix}a & b \\c & d \\\end{pmatrix}" />, maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}" /></span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}a&space;&&space;b&space;\\c&space;&&space;d&space;\\\end{pmatrix}\begin{pmatrix}-2&space;&&space;5&space;\\1&space;&&space;-3&space;\\\end{pmatrix}=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}a & b \\c & d \\\end{pmatrix}\begin{pmatrix}-2 & 5 \\1 & -3 \\\end{pmatrix}=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-2a+b&space;&&space;5a-3b&space;\\-2c+d&space;&&space;5c-3d&space;\\\end{pmatrix}=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-2a+b & 5a-3b \\-2c+d & 5c-3d \\\end{pmatrix}=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Dari kesamaan matriks diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;">*) Baris pertama kolom pertama</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>-</i>2<i>a</i> + <i>b</i> = 0 ........(1)</span></p><p style="text-align: left;"><span style="font-size: medium;">*) Baris pertama kolom kedua</span></p><p style="text-align: left;"><span style="font-size: medium;">5<i>a -</i> 3<i>b</i> = <i>-</i>1 .......(2)</span></p><p style="text-align: left;"><span style="font-size: medium;">*) Baris kedua kolom pertama</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>-</i>2<i>c</i> + <i>d</i> = <i>-</i>2 .......(3)</span></p><p style="text-align: left;"><span style="font-size: medium;">*) Baris kedua kolom kedua</span></p><p style="text-align: left;"><span style="font-size: medium;">5<i>c -</i> 3<i>d</i> = 3 .......(4)</span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">Eliminasi variabel <i>b</i> dari persamaan (1) dan (2)</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left.\begin{matrix}-2a+b=0\\5a-3b=-1\end{matrix}\right|\begin{matrix}x3&space;\\x1\end{matrix}" title="https://latex.codecogs.com/svg.image?\left.\begin{matrix}-2a+b=0\\5a-3b=-1\end{matrix}\right|\begin{matrix}x3 \\x1\end{matrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}-6a+3b=0\\\underline{5a-3b=-1}+\\-a=-1\\a=1\end{matrix}" title="https://latex.codecogs.com/svg.image?\begin{matrix}-6a+3b=0\\\underline{5a-3b=-1}+\\-a=-1\\a=1\end{matrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">Subtitusi <i>a</i> = 1 ke persamaan (1)</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>-</i>2<i>a + b</i> = 0</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>-</i>2.1 <i>+ b</i> = 0</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>b</i> = 2</span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">Eliminasi variabel <i>d</i> dari persamaan (3) dan (4)</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left.\begin{matrix}-2c+d=-2&space;\\5c-3d=3\end{matrix}\right|\begin{matrix}x3&space;\\x1\end{matrix}" title="https://latex.codecogs.com/svg.image?\left.\begin{matrix}-2c+d=-2 \\5c-3d=3\end{matrix}\right|\begin{matrix}x3 \\x1\end{matrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}-6c+3d=-6&space;\\\underline{5c-3d=3}+\\-c=-3\\c=3\end{matrix}" title="https://latex.codecogs.com/svg.image?\begin{matrix}-6c+3d=-6 \\\underline{5c-3d=3}+\\-c=-3\\c=3\end{matrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">Substitusi <i>c</i> = 3 ke persamaan (3)</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>-</i>2.3 + <i>d</i> = <i>-</i>2</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>-</i>6 + <i>d</i> = <i>-</i>2</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>d = -</i>2 + 6</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>d =</i> 4</span></p><p style="text-align: left;"><span style="font-size: medium;">Jadi matrik <i>K</i> adalah <img src="https://latex.codecogs.com/svg.image?K=\begin{pmatrix}1&space;&&space;2&space;\\3&space;&&space;4\end{pmatrix}" title="https://latex.codecogs.com/svg.image?K=\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Cara 2</b>. Menggunakan Invers matriks</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?KM=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?K=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}M^{-1}" title="https://latex.codecogs.com/svg.image?K=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}M^{-1}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}\frac{1}{detM}AdjM" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}\frac{1}{detM}AdjM" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}\frac{1}{6-5}\begin{pmatrix}-3&space;&&space;-5&space;\\-1&space;&&space;-2&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}\frac{1}{6-5}\begin{pmatrix}-3 & -5 \\-1 & -2 \\\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0&space;&&space;-1&space;\\-2&space;&&space;3&space;\\\end{pmatrix}\begin{pmatrix}-3&space;&&space;-5&space;\\-1&space;&&space;-2&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0 & -1 \\-2 & 3 \\\end{pmatrix}\begin{pmatrix}-3 & -5 \\-1 & -2 \\\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0(-3)+(-1(-1))&space;&&space;0(-5)+(-1)(-2)&space;\\(-2)(-3)+3(-1)&space;&&space;(-2)(-5)+3(-2)\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}0(-3)+(-1(-1)) & 0(-5)+(-1)(-2) \\(-2)(-3)+3(-1) & (-2)(-5)+3(-2)\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1&space;&&space;2&space;\\3&space;&&space;4\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : E</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Hasil kali <img src="https://latex.codecogs.com/svg.image?A\begin{pmatrix}5&space;&&space;-3&space;\\0&space;&&space;6&space;\\\end{pmatrix}=\begin{pmatrix}-10&space;&&space;30&space;\\35&space;&&space;27&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A\begin{pmatrix}5 & -3 \\0 & 6 \\\end{pmatrix}=\begin{pmatrix}-10 & 30 \\35 & 27 \\\end{pmatrix}" />, Matriks <i>A =</i> ....</span></p><p style="text-align: left;"><span style="font-size: medium;">
A. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1&space;&&space;-1&space;\\4&space;&&space;7&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1 & -1 \\4 & 7 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">
B. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-2&space;&&space;4&space;\\7&space;&&space;-1&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-2 & 4 \\7 & -1 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">
C. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}4&space;&&space;-2&space;\\7&space;&&space;-1&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}4 & -2 \\7 & -1 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">
D. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}7&space;&&space;2&space;\\-1&space;&&space;4&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}7 & 2 \\-1 & 4 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">
E. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}7&space;&&space;2&space;\\4&space;&&space;-1&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}7 & 2 \\4 & -1 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A\begin{pmatrix}5&space;&&space;-3&space;\\0&space;&&space;6&space;\\\end{pmatrix}=\begin{pmatrix}-10&space;&&space;30&space;\\35&space;&&space;27&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A\begin{pmatrix}5 & -3 \\0 & 6 \\\end{pmatrix}=\begin{pmatrix}-10 & 30 \\35 & 27 \\\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}-10&space;&&space;30&space;\\35&space;&&space;27&space;\\\end{pmatrix}\begin{pmatrix}5&space;&&space;-3&space;\\0&space;&&space;6&space;\\\end{pmatrix}^{-1}" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}-10 & 30 \\35 & 27 \\\end{pmatrix}\begin{pmatrix}5 & -3 \\0 & 6 \\\end{pmatrix}^{-1}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}-10&space;&&space;30&space;\\35&space;&&space;27&space;\\\end{pmatrix}\frac{1}{30}\begin{pmatrix}6&space;&&space;3&space;\\0&space;&&space;5&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}-10 & 30 \\35 & 27 \\\end{pmatrix}\frac{1}{30}\begin{pmatrix}6 & 3 \\0 & 5 \\\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A=\frac{1}{30}\begin{pmatrix}-10.6+30.0&space;&&space;-10.3+30.5&space;\\35.6+27.0&space;&&space;35.3+27.5\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A=\frac{1}{30}\begin{pmatrix}-10.6+30.0 & -10.3+30.5 \\35.6+27.0 & 35.3+27.5\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A=\frac{1}{30}\begin{pmatrix}-60&space;&&space;120&space;\\210&space;&&space;240\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A=\frac{1}{30}\begin{pmatrix}-60 & 120 \\210 & 240\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}-2&space;&&space;4&space;\\7&space;&&space;8\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}-2 & 4 \\7 & 8\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : Tidak ada yang benar</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>3. Jika </span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}4&space;&&space;2&space;\\5p+q&space;&&space;5&space;\\\end{pmatrix}=\begin{pmatrix}4&space;&&space;2&space;\\7&space;&&space;q+3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}4 & 2 \\5p+q & 5 \\\end{pmatrix}=\begin{pmatrix}4 & 2 \\7 & q+3 \\\end{pmatrix}" />, maka nilai <i>p</i> dan <i>q</i> adalah ....</span></p><p style="text-align: left;"><span style="font-size: medium;">A. <i>p =</i> 1 dan <i>q = -</i>2</span></p><p style="text-align: left;"><span style="font-size: medium;">B. <i>p =</i> 1 dan <i>q =</i> 2</span></p><p style="text-align: left;"><span style="font-size: medium;">C. <i>p =</i> -1 dan <i>q =</i> 2</span></p><p style="text-align: left;"><span style="font-size: medium;">D. <i>p =</i> 1 dan <i>q =</i> 8</span></p><p style="text-align: left;"><span style="font-size: medium;">E. <i>p =</i> 5 dan <i>q =</i> 2</span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dengan menggunakan kesamaan matriks sehingga diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}4&space;&&space;2&space;\\5p+q&space;&&space;5&space;\\\end{pmatrix}=\begin{pmatrix}4&space;&&space;2&space;\\7&space;&&space;q+3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}4 & 2 \\5p+q & 5 \\\end{pmatrix}=\begin{pmatrix}4 & 2 \\7 & q+3 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Dari baris kedua kolom kedua diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>q +</i> 3 = 5</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>q =</i> 5 - 3</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>q =</i> 2</span></p><p style="text-align: left;"><span style="font-size: medium;">Subtitusi <i>q = </i> 2 ke persamaan dari baris kedua kolom pertama</span></p><p style="text-align: left;"><span style="font-size: medium;">5<i>p</i> + <i>q</i> = 7</span></p><p style="text-align: left;"><span style="font-size: medium;">5<i>p</i> + 2 = 7</span></p><p style="text-align: left;"><span style="font-size: medium;">5<i>p =</i> 7 - 2</span></p><p style="text-align: left;"><span style="font-size: medium;">5<i>p =</i> 5</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>p =</i> 5/5</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>p =</i> 1</span></p><p style="text-align: left;"><span style="font-size: medium;">Jadi <i>p =</i> 1 dan <i>q =</i> 2</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Jika <img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}2&space;&&space;1&space;\\4&space;&&space;5&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}2 & 1 \\4 & 5 \\\end{pmatrix}" />,
<img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}1&space;&&space;0&space;\\3&space;&&space;4&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}1 & 0 \\3 & 4 \\\end{pmatrix}" /> dan
<img src="https://latex.codecogs.com/svg.image?C=\begin{pmatrix}-2&space;&&space;3&space;\\-1&space;&&space;4&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?C=\begin{pmatrix}-2 & 3 \\-1 & 4 \\\end{pmatrix}" />, maka (<i>A + </i>2<i>B</i>) - (2<i>B +</i> 2<i>C</i>) adalah ....</span></p><p style="text-align: left;"><span style="font-size: medium;">A. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}6&space;&&space;5&space;\\2&space;&&space;-6&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}6 & 5 \\2 & -6 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">
B. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}6&space;&&space;-5&space;\\6&space;&&space;-3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}6 & -5 \\6 & -3 \\\end{pmatrix}" /> </span></p><p style="text-align: left;"><span style="font-size: medium;">C. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}6&space;&&space;-5&space;\\6&space;&&space;13&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}6 & -5 \\6 & 13 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">
D. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}6&space;&&space;-5&space;\\6&space;&&space;1&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}6 & -5 \\6 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">E. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}6&space;&&space;-5&space;\\2&space;&&space;-3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}6 & -5 \\2 & -3 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;">(<i>A + </i>2<i>B</i>) - (2<i>B +</i> 2<i>C</i>)</span></p><p style="text-align: left;"><span style="font-size: medium;">= <i>A + </i>2<i>B -</i> 2<i>B + </i>2<i>C</i></span></p><p style="text-align: left;"><span style="font-size: medium;">= <i>A +</i> 2<i>C</i></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2&space;&&space;1&space;\\4&space;&&space;5&space;\\\end{pmatrix}-2\begin{pmatrix}-2&space;&&space;3&space;\\-1&space;&&space;4&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2 & 1 \\4 & 5 \\\end{pmatrix}-2\begin{pmatrix}-2 & 3 \\-1 & 4 \\\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2&space;&&space;1&space;\\4&space;&&space;5&space;\\\end{pmatrix}-\begin{pmatrix}-4&space;&&space;6&space;\\-2&space;&&space;8&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2 & 1 \\4 & 5 \\\end{pmatrix}-\begin{pmatrix}-4 & 6 \\-2 & 8 \\\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2+4&space;&&space;1-6&space;\\4+2&space;&&space;5-8&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2+4 & 1-6 \\4+2 & 5-8 \\\end{pmatrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}6&space;&&space;-5&space;\\6&space;&&space;-3&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}6 & -5 \\6 & -3 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>5. Diketahui </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}2a&space;&&space;4&space;&&space;6&space;\\8&space;&&space;10&space;&&space;b&space;\\4c&space;&&space;5&space;&&space;12&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}2a & 4 & 6 \\8 & 10 & b \\4c & 5 & 12 \\\end{pmatrix}" /> dan
<img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}8&space;&&space;4&space;&&space;6&space;\\8&space;&&space;10&space;&&space;4a&space;\\b&space;&&space;5&space;&&space;12&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}8 & 4 & 6 \\8 & 10 & 4a \\b & 5 & 12 \\\end{pmatrix}" />. Jika <i>A = B</i>, maka <i>c</i> = ....</span></p><p style="text-align: left;"><span style="font-size: medium;">A. 3</span></p><p style="text-align: left;"><span style="font-size: medium;">B. 4</span></p><p style="text-align: left;"><span style="font-size: medium;">C. 5</span></p><p style="text-align: left;"><span style="font-size: medium;">D. 6</span></p><p style="text-align: left;"><span style="font-size: medium;">E. 7</span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dua buah matriks dikatakan sama jika memiliki ordo sama dan elemen-elemen yang bersesuaian sama.</span></p><p style="text-align: left;"><i><span style="font-size: medium;">A = B</span></i></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}2a&space;&&space;4&space;&&space;6&space;\\8&space;&&space;10&space;&&space;b&space;\\4c&space;&&space;5&space;&&space;12&space;\\\end{pmatrix}=\begin{pmatrix}8&space;&&space;4&space;&&space;6&space;\\8&space;&&space;10&space;&&space;4a&space;\\b&space;&&space;5&space;&&space;12&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}2a & 4 & 6 \\8 & 10 & b \\4c & 5 & 12 \\\end{pmatrix}=\begin{pmatrix}8 & 4 & 6 \\8 & 10 & 4a \\b & 5 & 12 \\\end{pmatrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">dari kesamaan matriks diatas diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;">*) Baris pertama kolom pertama</span></p><p style="text-align: left;"><span style="font-size: medium;">2<i>a =</i> 8</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>a =</i> 8/2</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>a =</i> 4</span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">*) Baris kedua kolom ketiga</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>b =</i> 4<i>a</i></span></p><p style="text-align: left;"><span style="font-size: medium;"><i>b =</i> 4.4</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>b =</i> 16</span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">*) Baris ketiga kolom pertama</span></p><p style="text-align: left;"><span style="font-size: medium;">4<i>c = b</i></span></p><p style="text-align: left;"><span style="font-size: medium;">4<i>c =</i> 16</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>c =</i> 16/4</span></p><p style="text-align: left;"><span style="font-size: medium;"><i>c =</i> 4</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span>6. Jika matriks </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}a&space;&&space;2&space;&&space;3&space;\\1&space;&&space;a&space;&&space;4&space;\\a&space;&&space;2&space;&&space;5&space;\\\end{pmatrix}" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}a & 2 & 3 \\1 & a & 4 \\a & 2 & 5 \\\end{pmatrix}" /> tidak memiliki invers maka nilai <i>a = </i>....</span></p><p style="text-align: left;">
<span style="font-size: medium;">A. -2 atau 2</span></p><p style="text-align: left;"><span style="font-size: medium;">B. <img src="https://latex.codecogs.com/svg.image?-\sqrt{2}" title="https://latex.codecogs.com/svg.image?-\sqrt{2}" /> atau <img src="https://latex.codecogs.com/svg.image?\sqrt{2}" title="https://latex.codecogs.com/svg.image?\sqrt{2}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;">C. -1 atau 1</span></p><p style="text-align: left;"><span style="font-size: medium;">D. 2</span></p><p style="text-align: left;"><span style="font-size: medium;">E. <img src="https://latex.codecogs.com/svg.image?2\sqrt{2}" title="https://latex.codecogs.com/svg.image?2\sqrt{2}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Suatu matriks dikatakan tidak memiliki invers jika determinannya sama dengan nol.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?detA=\begin{vmatrix}a&space;&&space;2&space;&&space;3&space;\\1&space;&&space;a&space;&&space;4&space;\\a&space;&&space;2&space;&&space;5&space;\\\end{vmatrix}=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?detA=\begin{vmatrix}a & 2 & 3 \\1 & a & 4 \\a & 2 & 5 \\\end{vmatrix}=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{vmatrix}a&space;&&space;2&space;&&space;3&space;\\1&space;&&space;a&space;&&space;4&space;\\a&space;&&space;2&space;&&space;5&space;\\\end{vmatrix}\begin{matrix}a&space;&&space;2&space;\\1&space;&&space;a&space;\\a&space;&&space;2&space;\\\end{matrix}=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{vmatrix}a & 2 & 3 \\1 & a & 4 \\a & 2 & 5 \\\end{vmatrix}\begin{matrix}a & 2 \\1 & a \\a & 2 \\\end{matrix}=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?a.a.5+2.4.a+3.1.2-3.a.a-a.4.a-2.1.5=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?a.a.5+2.4.a+3.1.2-3.a.a-a.4.a-2.1.5=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?5a^{2}+8a+6-3a^{2}-8a-10=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?5a^{2}+8a+6-3a^{2}-8a-10=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?5a^{2}-3a^{2}+8a-8a+6-10=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?5a^{2}-3a^{2}+8a-8a+6-10=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?2a^{2}-4=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?2a^{2}-4=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?a^{2}-2=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?a^{2}-2=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\left&space;(&space;a+\sqrt{2}&space;\right&space;)\left&space;(&space;a-\sqrt{2}&space;\right&space;)=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\left ( a+\sqrt{2} \right )\left ( a-\sqrt{2} \right )=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\left&space;(&space;a+\sqrt{2}&space;\right&space;)=0\,&space;\,&space;atau\,&space;\,&space;\left&space;(&space;a-\sqrt{2}&space;\right&space;)=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\left ( a+\sqrt{2} \right )=0\, \, atau\, \, \left ( a-\sqrt{2} \right )=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?a=-\sqrt{2}\,&space;\,&space;atau\,&space;\,&space;a=\sqrt{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?a=-\sqrt{2}\, \, atau\, \, a=\sqrt{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>7. Jika </span><span style="text-align: left;"> </span><img src="https://latex.codecogs.com/svg.image?2\begin{pmatrix}-1&space;\\\frac{1}{2}&space;\\\frac{1}{2}\end{pmatrix}+3\begin{pmatrix}4&space;\\0&space;\\3\end{pmatrix}+k\begin{pmatrix}2&space;\\1&space;\\3\end{pmatrix}=\begin{pmatrix}2&space;\\-3&space;\\-4\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?2\begin{pmatrix}-1 \\\frac{1}{2} \\\frac{1}{2}\end{pmatrix}+3\begin{pmatrix}4 \\0 \\3\end{pmatrix}+k\begin{pmatrix}2 \\1 \\3\end{pmatrix}=\begin{pmatrix}2 \\-3 \\-4\end{pmatrix}" />, maka k adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. -4</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. -2</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 4</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil salah satu baris yang sama dari operasi matriks diatas. Misal akan diambil baris pertama dan dengan menggunaan kesamaan matriks diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">2(-1) + 3(4) + 2<i>k</i> = 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">-2 + 12 + 2<i>k</i> = 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">10 + 2<i>k</i> = 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">2<i>k</i> = 2 - 10</span></p><p style="text-align: justify;"><span style="font-size: medium;">2<i>k</i> = -8</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>k</i> = -8/2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>k</i> = -4</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>8. Diketahui </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}" /> dan <span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?I=\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?I=\begin{pmatrix}1 & 0 \\0 & 1 \\\end{pmatrix}" /><span style="text-align: left;"> .</span></span></p><p style="text-align: justify;"><span style="font-size: medium;">(1) <img src="https://latex.codecogs.com/svg.image?AI=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AI=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>(2) <img src="https://latex.codecogs.com/svg.image?IA=\begin{pmatrix}3&space;&&space;2&space;\\5&space;&&space;4&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?IA=\begin{pmatrix}3 & 2 \\5 & 4 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">(3) <i>I . I = I</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">(4) <i>AA = A</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">Pernyataan yang benar adalah....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. (1), (2)</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. (1), (3)</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. (2), (4)</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. (1), (4)</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. (3), (4)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>AI = IA = A</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>I . I = I</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i><span>AA </span><img src="https://latex.codecogs.com/svg.image?\neq&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\neq" /> A</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi pernyataan yang benar adalah (1) dan (3)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>9. Jika diketahui dua buah matriks </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1&space;&&space;3&space;\\4&space;&&space;-3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1 & 3 \\4 & -3 \\\end{pmatrix}" /><span style="text-align: left;"> dan </span><img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}3&space;\\2\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}3 \\2\end{pmatrix}" />, maka yang benar diantara hubungan berikut adalah....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. <i>BA =</i> 3<i>B</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">B. <i>BA = </i>3<i>A</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">C. <i>AB =</i> 3<i>B</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">D. <i>AB =</i> 3<i>A</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 3<i>AB = B</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Matriks <i>A</i> berordo 2x2 dan matriks <i>B</i> berordo 2x1, maka operasi yang bisa dilakukan adalah <i>AB</i> dan menghasilkan matriks ordo 2x1, sedangkan <i>BA</i> tidak bisa dilakukan. Sehingga kemungkinan yang benar adalah C atau E. Mari kita cek operasi <i>AB</i>.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?AB=\begin{pmatrix}1&space;&&space;3&space;\\4&space;&&space;-3&space;\\\end{pmatrix}\begin{pmatrix}3&space;\\2\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AB=\begin{pmatrix}1 & 3 \\4 & -3 \\\end{pmatrix}\begin{pmatrix}3 \\2\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1.3+3.2&space;\\4.3-3.2\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1.3+3.2 \\4.3-3.2\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}9&space;\\6\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}9 \\6\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=3\begin{pmatrix}3&space;\\2\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=3\begin{pmatrix}3 \\2\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dari operasi diatas jelas terlihat bahwa <i>AB =</i> 3<i>B</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>10. Diketahui matriks <i>A</i> dan matriks <i>B</i> berordo 2x2. Matriks </span><img src="https://latex.codecogs.com/svg.image?(A+B)^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?(A+B)^{2}" /><span> senilai dengan .....</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>A. </span><img src="https://latex.codecogs.com/svg.image?A^{2}+2AB+B^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A^{2}+2AB+B^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?A^{2}+AB+AB+B^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A^{2}+AB+AB+B^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?AA+2AB+BB" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AA+2AB+BB" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?A(A+B)+B(A+B)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A(A+B)+B(A+B)" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>E. <img src="https://latex.codecogs.com/svg.image?A^{2}+2BA+B^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A^{2}+2BA+B^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><span style="text-align: left;"></span>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left&space;(&space;&space;A+B\right&space;)^{2}=\left&space;(&space;A+B&space;\right&space;)\left&space;(&space;A+B&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\left ( A+B\right )^{2}=\left ( A+B \right )\left ( A+B \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?=A\left&space;(&space;A+B&space;\right&space;)+B\left&space;(&space;A+B&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=A\left ( A+B \right )+B\left ( A+B \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?=AA+AB+BA+BB" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=AA+AB+BA+BB" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?=A^{2}+AB+BA+B^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=A^{2}+AB+BA+B^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>Ingat bahwa <img src="https://latex.codecogs.com/svg.image?AB\neq&space;BA" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AB\neq BA" />, <img src="https://latex.codecogs.com/svg.image?AA=A^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AA=A^{2}" /> dan <img src="https://latex.codecogs.com/svg.image?BB=B^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?BB=B^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>11. Jika </span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1&space;&&space;d&space;\\-b&space;&&space;3&space;\\\end{pmatrix}+\begin{pmatrix}4&space;&&space;-5&space;\\-3&space;&&space;b&space;\\\end{pmatrix}=\begin{pmatrix}2&space;&&space;-1&space;\\-4&space;&&space;3&space;\\\end{pmatrix}\begin{pmatrix}2c&space;&&space;1&space;\\c&space;&&space;a+1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1 & d \\-b & 3 \\\end{pmatrix}+\begin{pmatrix}4 & -5 \\-3 & b \\\end{pmatrix}=\begin{pmatrix}2 & -1 \\-4 & 3 \\\end{pmatrix}\begin{pmatrix}2c & 1 \\c & a+1 \\\end{pmatrix}" />, maka <i>a =</i> .....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>A. -2</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. <img src="https://latex.codecogs.com/svg.image?-\frac{4}{3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?-\frac{4}{3}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?\frac{2}{3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\frac{2}{3}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. <img src="https://latex.codecogs.com/svg.image?-\frac{2}{3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?-\frac{2}{3}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1&space;&&space;d&space;\\-b&space;&&space;3&space;\\\end{pmatrix}+\begin{pmatrix}4&space;&&space;-5&space;\\-3&space;&&space;b&space;\\\end{pmatrix}=\begin{pmatrix}2&space;&&space;-1&space;\\-4&space;&&space;3&space;\\\end{pmatrix}\begin{pmatrix}2c&space;&&space;1&space;\\c&space;&&space;a+1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1 & d \\-b & 3 \\\end{pmatrix}+\begin{pmatrix}4 & -5 \\-3 & b \\\end{pmatrix}=\begin{pmatrix}2 & -1 \\-4 & 3 \\\end{pmatrix}\begin{pmatrix}2c & 1 \\c & a+1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1+4&space;&&space;d-5&space;\\-b-3&space;&&space;3+b&space;\\\end{pmatrix}=\begin{pmatrix}2.2c-1.c&space;&&space;2.1-1(a+1)&space;\\-4.2c+3.c&space;&&space;-4.1+3(a+1)&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1+4 & d-5 \\-b-3 & 3+b \\\end{pmatrix}=\begin{pmatrix}2.2c-1.c & 2.1-1(a+1) \\-4.2c+3.c & -4.1+3(a+1) \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}3&space;&&space;d-5&space;\\-b-3&space;&&space;3+b&space;\\\end{pmatrix}=\begin{pmatrix}3c&space;&&space;-a+1&space;\\-5c&space;&&space;3a-1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}3 & d-5 \\-b-3 & 3+b \\\end{pmatrix}=\begin{pmatrix}3c & -a+1 \\-5c & 3a-1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Berdasarkan kesamaan dua matriks diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">*) Baris pertama Kolom pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;">3 = 3<i>c</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>c</i> = 3/3</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>c</i> = 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">*) Baris kedua kolom pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>-b -</i> 3 = <i>-</i>5<i>c</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>-b -</i> 3 = <i>-</i>5 . 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>-b -</i> 3 = <i>-</i>5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>-b</i> = <i>-</i>5 + 3</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>-b</i> = <i>-</i>2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>b</i> = 2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">*) Baris kedua kolom kedua</span></p><p style="text-align: justify;"><span style="font-size: medium;">3<i>+b =</i> 3<i>a -</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">3 + 2 = 3<i>a -</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">3<i>a -</i> 1 = 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">3<i>a =</i> 5 + 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">3<i>a =</i> 6</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>a =</i> 6/3</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>a =</i> 2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>12. Jika </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1&space;&&space;1&space;\\-1&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1 & 1 \\-1 & 1 \\\end{pmatrix}" /> dan<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}0&space;&&space;1&space;\\1&space;&&space;0&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}0 & 1 \\1 & 0 \\\end{pmatrix}" /> maka (<i>A + B</i>)(<i>A - B</i>) <i>-</i> (<i>A - B</i>)(<i>A + B</i>) = .....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>A. </span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}0&space;&&space;0&space;\\0&space;&&space;0&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}0 & 0 \\0 & 0 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-1 & 0 \\0 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?4\begin{pmatrix}-1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?4\begin{pmatrix}-1 & 0 \\0 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?8\begin{pmatrix}-1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?8\begin{pmatrix}-1 & 0 \\0 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>E. <img src="https://latex.codecogs.com/svg.image?16\begin{pmatrix}-1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?16\begin{pmatrix}-1 & 0 \\0 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>(</span><i>A + B</i><span>)(</span><i>A - B</i><span>) </span><i>-</i><span> (</span><i>A - B</i><span>)(</span><i>A + B</i><span>)</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>= A(A - B) + B(A - B) - (A(A + B) - B(A + B))</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>= AA - AB + BA - BB -(AA + AB - BA - BB)</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>= AA - AB + BA - BB -AA - AB + BA + BB</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>= AA - AA - AB - AB + BA + BA - BB + BB</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>= - AB - AB + BA + BA</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>= -</i>2<i>AB + </i>2<i>BA</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=-2\begin{pmatrix}1&space;&&space;1&space;\\-1&space;&&space;1&space;\\\end{pmatrix}\begin{pmatrix}0&space;&&space;1&space;\\1&space;&&space;0&space;\\\end{pmatrix}+2\begin{pmatrix}0&space;&&space;1&space;\\1&space;&&space;0&space;\\\end{pmatrix}\begin{pmatrix}1&space;&&space;1&space;\\-1&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=-2\begin{pmatrix}1 & 1 \\-1 & 1 \\\end{pmatrix}\begin{pmatrix}0 & 1 \\1 & 0 \\\end{pmatrix}+2\begin{pmatrix}0 & 1 \\1 & 0 \\\end{pmatrix}\begin{pmatrix}1 & 1 \\-1 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?=-2\begin{pmatrix}1&space;&&space;1&space;\\1&space;&&space;-1&space;\\\end{pmatrix}+2\begin{pmatrix}-1&space;&&space;1&space;\\1&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=-2\begin{pmatrix}1 & 1 \\1 & -1 \\\end{pmatrix}+2\begin{pmatrix}-1 & 1 \\1 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-2&space;&&space;-2&space;\\-2&space;&&space;2&space;\\\end{pmatrix}+\begin{pmatrix}-2&space;&&space;2&space;\\2&space;&&space;2&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-2 & -2 \\-2 & 2 \\\end{pmatrix}+\begin{pmatrix}-2 & 2 \\2 & 2 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-4&space;&&space;0&space;\\0&space;&&space;4&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-4 & 0 \\0 & 4 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?=4\begin{pmatrix}-1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=4\begin{pmatrix}-1 & 0 \\0 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>13. Diketahui </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1&space;&&space;2&space;\\3&space;&&space;4&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1 & 2 \\3 & 4 \\\end{pmatrix}" /> dan<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?I=\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?I=\begin{pmatrix}1 & 0 \\0 & 1 \\\end{pmatrix}" /> jika<span style="text-align: left;"> </span><img src="https://latex.codecogs.com/svg.image?A^{2}=pA+qI" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A^{2}=pA+qI" />, maka nilai <i>p</i> dan <i>q</i> adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. <i>p =</i> 5 dan <i>q = </i>2</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. <i>p =</i> 5 dan <i>q = -</i>2</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. <i>p = -</i>5 dan <i>q =</i> 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. <i>p =</i> 2 dan <i>q = -</i>5</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. <i>p =</i> 2 dan <i>q =</i> 5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A^{2}=pA+qI" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A^{2}=pA+qI" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>AA = pA + qI</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}1&space;&&space;2&space;\\3&space;&&space;4&space;\\\end{pmatrix}\begin{pmatrix}1&space;&&space;2&space;\\3&space;&&space;4&space;\\\end{pmatrix}=p\begin{pmatrix}1&space;&&space;2&space;\\3&space;&&space;4&space;\\\end{pmatrix}+q\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}1 & 2 \\3 & 4 \\\end{pmatrix}\begin{pmatrix}1 & 2 \\3 & 4 \\\end{pmatrix}=p\begin{pmatrix}1 & 2 \\3 & 4 \\\end{pmatrix}+q\begin{pmatrix}1 & 0 \\0 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}7&space;&&space;10&space;\\15&space;&&space;22&space;\\\end{pmatrix}=\begin{pmatrix}p&space;&&space;2p&space;\\3p&space;&&space;4p&space;\\\end{pmatrix}+\begin{pmatrix}q&space;&&space;0&space;\\0&space;&&space;q&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}7 & 10 \\15 & 22 \\\end{pmatrix}=\begin{pmatrix}p & 2p \\3p & 4p \\\end{pmatrix}+\begin{pmatrix}q & 0 \\0 & q \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}7&space;&&space;10&space;\\15&space;&&space;22&space;\\\end{pmatrix}=\begin{pmatrix}p+q&space;&&space;2p&space;\\3p&space;&&space;4p+q&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}7 & 10 \\15 & 22 \\\end{pmatrix}=\begin{pmatrix}p+q & 2p \\3p & 4p+q \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dengan menggunakan kesamaan dua matriks diperoleh :</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dari baris pertama kolom kedua</span></p><p style="text-align: justify;"><span style="font-size: medium;">10 = 2<i>p</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>p =</i> 10/2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>p =</i> 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dari baris pertama kolom pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;">7 <i>= p + q</i></span></p><p style="text-align: justify;"><span style="font-size: medium;">5 <i>+ q =</i> 7</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>q =</i> 7 - 5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>q =</i> 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi <i>p =</i> 5 dan <i>q =</i> 2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>14. Diketahui matriks </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1&space;&&space;a+b&space;\\b&space;&&space;c&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1 & a+b \\b & c \\\end{pmatrix}" />,<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}a-1&space;&&space;0&space;\\-c&space;&&space;d&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}a-1 & 0 \\-c & d \\\end{pmatrix}" /> dan<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?C=\begin{pmatrix}1&space;&&space;0&space;\\1&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?C=\begin{pmatrix}1 & 0 \\1 & 1 \\\end{pmatrix}" />. Jika<span style="text-align: left;"> </span><img src="https://latex.codecogs.com/svg.image?A+B^{T}=C^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A+B^{T}=C^{2}" />, dengan<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?B^{T}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?B^{T}" /> adalah transpose matriks <i>B</i>, maka <i>d =</i>....</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">A. -1</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">B. -2</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">C. 0</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">D. 1</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">E. 2</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui <img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1&space;&&space;a+b&space;\\b&space;&&space;c&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1 & a+b \\b & c \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}a-1&space;&&space;0&space;\\-c&space;&&space;d&space;\\\end{pmatrix}\Leftrightarrow&space;B^{T}=\begin{pmatrix}a-1&space;&&space;-c&space;\\0&space;&&space;d&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}a-1 & 0 \\-c & d \\\end{pmatrix}\Leftrightarrow B^{T}=\begin{pmatrix}a-1 & -c \\0 & d \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?C=\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}\Leftrightarrow&space;C^{2}=\begin{pmatrix}1&space;&&space;0&space;\\1&space;&&space;1&space;\\\end{pmatrix}\begin{pmatrix}1&space;&&space;0&space;\\1&space;&&space;1&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;0&space;\\2&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?C=\begin{pmatrix}1 & 0 \\0 & 1 \\\end{pmatrix}\Leftrightarrow C^{2}=\begin{pmatrix}1 & 0 \\1 & 1 \\\end{pmatrix}\begin{pmatrix}1 & 0 \\1 & 1 \\\end{pmatrix}=\begin{pmatrix}1 & 0 \\2 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A+B^{T}=C^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A+B^{T}=C^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}1&space;&&space;a+b&space;\\b&space;&&space;c&space;\\\end{pmatrix}+\begin{pmatrix}a-1&space;&&space;-c&space;\\0&space;&&space;d&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;0&space;\\2&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}1 & a+b \\b & c \\\end{pmatrix}+\begin{pmatrix}a-1 & -c \\0 & d \\\end{pmatrix}=\begin{pmatrix}1 & 0 \\2 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}1+a-1&space;&&space;a+b-c&space;\\b&space;&&space;c+d&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;0&space;\\2&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}1+a-1 & a+b-c \\b & c+d \\\end{pmatrix}=\begin{pmatrix}1 & 0 \\2 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}a&space;&&space;a+b-c&space;\\b&space;&&space;c+d&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;0&space;\\2&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}a & a+b-c \\b & c+d \\\end{pmatrix}=\begin{pmatrix}1 & 0 \\2 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Berdasarkan kesamaan dua matriks diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">*) dari baris pertama kolom pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>a =</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">*) dari baris kedua kolom pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>b =</i> 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">*) dari baris pertama kolom kedua</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>a + b - c =</i> 0</span></p><p style="text-align: justify;"><span style="font-size: medium;">1 + 2 <i>- c =</i> 0</span></p><p style="text-align: justify;"><span style="font-size: medium;">3 <i>- c =</i> 0</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>-c = -</i>3</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>c =</i> 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">*) dari baris kedua kolom kedua</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>c + d =</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">3 <i>+ d =</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>d = </i>1 <i>-</i> 3</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>d = -</i>2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">15. Diketahui matriks <img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1&space;&&space;2&space;\\4&space;&&space;3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}1 & 2 \\4 & 3 \\\end{pmatrix}" />, bilangan <i>x</i> yang memenuhi persamaan |<i>A - xI</i>| = 0 jika |<i>A - xI</i>| determinan dari <i>A - xI</i> adalah .....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. -1 atau 0</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 5 atau 0</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 1 atau 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. -1 atau 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. -1 atau -5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?A-xI=\begin{pmatrix}1&space;&&space;2&space;\\4&space;&&space;3&space;\\\end{pmatrix}-x\begin{pmatrix}1&space;&&space;0&space;\\0&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A-xI=\begin{pmatrix}1 & 2 \\4 & 3 \\\end{pmatrix}-x\begin{pmatrix}1 & 0 \\0 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1&space;&&space;2&space;\\4&space;&&space;3&space;\\\end{pmatrix}-\begin{pmatrix}x&space;&&space;0&space;\\0&space;&&space;x&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1 & 2 \\4 & 3 \\\end{pmatrix}-\begin{pmatrix}x & 0 \\0 & x \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1-x&space;&&space;2&space;\\4&space;&&space;3-x&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}1-x & 2 \\4 & 3-x \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sementara diketahui juga</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>|</span><i>A - xI</i><span>| = 0</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{vmatrix}1-x&space;&&space;2&space;\\4&space;&&space;3-x&space;\\\end{vmatrix}=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{vmatrix}1-x & 2 \\4 & 3-x \\\end{vmatrix}=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?(1-x)(3-x)-2.4=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?(1-x)(3-x)-2.4=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?3-x-3x+x^{2}-8=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?3-x-3x+x^{2}-8=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?-4x+x^{2}-5=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?-4x+x^{2}-5=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?x^{2}-4x-5=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x^{2}-4x-5=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?(x-5)(x+1)=0" style="text-align: left;" title="https://latex.codecogs.com/svg.image?(x-5)(x+1)=0" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?x=5\,&space;\,&space;\textrm{atau}\,&space;\,&space;x=-1" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x=5\, \, \textrm{atau}\, \, x=-1" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>16. Jika </span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}4&space;&&space;1&space;\\3&space;&&space;a&space;\\\end{pmatrix}\begin{pmatrix}-1&space;&&space;a&space;\\2a&space;+&space;b&space;&&space;7&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;15&space;\\7&space;&&space;20&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}4 & 1 \\3 & a \\\end{pmatrix}\begin{pmatrix}-1 & a \\2a + b & 7 \\\end{pmatrix}=\begin{pmatrix}1 & 15 \\7 & 20 \\\end{pmatrix}" />, maka <i>b =</i> ....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>A. 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 4</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}4&space;&&space;1&space;\\3&space;&&space;a&space;\\\end{pmatrix}\begin{pmatrix}-1&space;&&space;a&space;\\2a&space;+&space;b&space;&&space;7&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;15&space;\\7&space;&&space;20&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}4 & 1 \\3 & a \\\end{pmatrix}\begin{pmatrix}-1 & a \\2a + b & 7 \\\end{pmatrix}=\begin{pmatrix}1 & 15 \\7 & 20 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}4(-1)+1(2a+b)&space;&&space;4(a)+1(7)&space;\\3(-1)+a(2a+b)&space;&&space;3(a)+a(7)&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;15&space;\\7&space;&&space;20&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}4(-1)+1(2a+b) & 4(a)+1(7) \\3(-1)+a(2a+b) & 3(a)+a(7) \\\end{pmatrix}=\begin{pmatrix}1 & 15 \\7 & 20 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-4+2a+b&space;&&space;4a+7&space;\\-3+2a^{2}+ab&space;&&space;10a&space;\\\end{pmatrix}=\begin{pmatrix}1&space;&&space;15&space;\\7&space;&&space;20&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-4+2a+b & 4a+7 \\-3+2a^{2}+ab & 10a \\\end{pmatrix}=\begin{pmatrix}1 & 15 \\7 & 20 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">*) Dari baris kedua kolom kedua</span></p><p style="text-align: justify;"><span style="font-size: medium;">10<i>a =</i> 20</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>a =</i> 20/10</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>a =</i> 2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">*) dari baris pertama kolom pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;">-4 + 2a + <i>b =</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">-4 + 2(2) + <i>b =</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">-4 + 4 + <i>b =</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>b =</i> 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>17. Jika </span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}x&space;\\&space;y\end{pmatrix}=\begin{pmatrix}3&space;&&space;-2&space;\\1&space;&&space;1&space;\\\end{pmatrix}\begin{pmatrix}a&space;\\&space;b\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}x \\ y\end{pmatrix}=\begin{pmatrix}3 & -2 \\1 & 1 \\\end{pmatrix}\begin{pmatrix}a \\ b\end{pmatrix}" /> dan<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}a&space;\\&space;b\end{pmatrix}=\begin{pmatrix}2&space;&&space;3&space;\\5&space;&&space;-2&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}a \\ b\end{pmatrix}=\begin{pmatrix}2 & 3 \\5 & -2 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /> maka<span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}x&space;\\&space;y\end{pmatrix}=...." style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}x \\ y\end{pmatrix}=...." /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>A. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}5&space;&&space;1&space;\\6&space;&&space;-1&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}5 & 1 \\6 & -1 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}6&space;&&space;-6&space;\\5&space;&&space;-2&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}6 & -6 \\5 & -2 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-4&space;&&space;13&space;\\7&space;&&space;1&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-4 & 13 \\7 & 1 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}9&space;&&space;-1&space;\\13&space;&&space;-12&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}9 & -1 \\13 & -12 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>E. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}1&space;&&space;-5&space;\\-4&space;&&space;3&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}1 & -5 \\-4 & 3 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><span style="text-align: left;"></span>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}x&space;\\&space;y\end{pmatrix}=\begin{pmatrix}3&space;&&space;-2&space;\\1&space;&&space;1&space;\\\end{pmatrix}\begin{pmatrix}a&space;\\&space;b\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}x \\ y\end{pmatrix}=\begin{pmatrix}3 & -2 \\1 & 1 \\\end{pmatrix}\begin{pmatrix}a \\ b\end{pmatrix}" /> dan<span style="text-align: left;"> </span><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}a&space;\\&space;b\end{pmatrix}=\begin{pmatrix}2&space;&&space;3&space;\\5&space;&&space;-2&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}a \\ b\end{pmatrix}=\begin{pmatrix}2 & 3 \\5 & -2 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}x&space;\\&space;y\end{pmatrix}=\begin{pmatrix}3&space;&&space;-2&space;\\1&space;&&space;1&space;\\\end{pmatrix}\begin{pmatrix}2&space;&&space;3&space;\\5&space;&&space;-1&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}x \\ y\end{pmatrix}=\begin{pmatrix}3 & -2 \\1 & 1 \\\end{pmatrix}\begin{pmatrix}2 & 3 \\5 & -1 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3(2)-2(5)&space;&&space;3(3)+(-2)(-2)&space;\\1(2)+1(5)&space;&&space;1(3)+1(-2)&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3(2)-2(5) & 3(3)+(-2)(-2) \\1(2)+1(5) & 1(3)+1(-2) \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}6-10&space;&&space;9+4&space;\\2+5&space;&&space;3-2&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}6-10 & 9+4 \\2+5 & 3-2 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-4&space;&&space;13&space;\\7&space;&&space;1&space;\\\end{pmatrix}\begin{pmatrix}p&space;\\&space;q\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}-4 & 13 \\7 & 1 \\\end{pmatrix}\begin{pmatrix}p \\ q\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>18. Jika </span><img src="https://latex.codecogs.com/svg.image?P\begin{pmatrix}6&space;&&space;7&space;\\8&space;&&space;9&space;\\\end{pmatrix}=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?P\begin{pmatrix}6 & 7 \\8 & 9 \\\end{pmatrix}=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}" /> maka P = ....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>A. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}3&space;&&space;2&space;\\2&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}3 & 2 \\2 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}-3&space;&&space;2&space;\\-2&space;&&space;1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}-3 & 2 \\-2 & 1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}1&space;&&space;2&space;\\2&space;&&space;3&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}1 & 2 \\2 & 3 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}2&space;&&space;3&space;\\1&space;&&space;2&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}2 & 3 \\1 & 2 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>E. <img src="https://latex.codecogs.com/svg.image?\begin{pmatrix}3&space;&&space;-2&space;\\2&space;&&space;-1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{pmatrix}3 & -2 \\2 & -1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><span style="text-align: left;"></span>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?P\begin{pmatrix}6&space;&&space;7&space;\\8&space;&&space;9&space;\\\end{pmatrix}=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?P\begin{pmatrix}6 & 7 \\8 & 9 \\\end{pmatrix}=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal <img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}6&space;&&space;7&space;\\8&space;&&space;9&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}6 & 7 \\8 & 9 \\\end{pmatrix}" /><span style="text-align: left;"> dan </span><img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}" /> maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?PA=B" style="text-align: left;" title="https://latex.codecogs.com/svg.image?PA=B" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?PA.A^{-1}=B.A^{-1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?PA.A^{-1}=B.A^{-1}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?P=B.A^{-1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?P=B.A^{-1}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?P=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}\frac{1}{(6)(9)-(7)(8)}\begin{pmatrix}9&space;&&space;-7&space;\\-8&space;&&space;6&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?P=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}\frac{1}{(6)(9)-(7)(8)}\begin{pmatrix}9 & -7 \\-8 & 6 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}\frac{1}{54-56}\begin{pmatrix}9&space;&&space;-7&space;\\-8&space;&&space;6&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}\frac{1}{54-56}\begin{pmatrix}9 & -7 \\-8 & 6 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}\frac{1}{-2}\begin{pmatrix}9&space;&&space;-7&space;\\-8&space;&&space;6&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}\frac{1}{-2}\begin{pmatrix}9 & -7 \\-8 & 6 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}2&space;&&space;3&space;\\4&space;&&space;5&space;\\\end{pmatrix}\begin{pmatrix}9&space;&&space;-7&space;\\-8&space;&&space;6&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}2 & 3 \\4 & 5 \\\end{pmatrix}\begin{pmatrix}9 & -7 \\-8 & 6 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}(2)(9)+3(-8)&space;&&space;(2)(-7)+&space;(3)(6)&space;\\(4)(9)+5(-8)&space;&&space;(4)(-7)+(5)(6)&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}(2)(9)+3(-8) & (2)(-7)+ (3)(6) \\(4)(9)+5(-8) & (4)(-7)+(5)(6) \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}18-24&space;&&space;-14+18&space;\\36-40&space;&&space;-28+30&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}18-24 & -14+18 \\36-40 & -28+30 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}-6&space;&&space;4&space;\\-4&space;&&space;2&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=-\frac{1}{2}\begin{pmatrix}-6 & 4 \\-4 & 2 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3&space;&&space;-2&space;\\2&space;&&space;-1&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\begin{pmatrix}3 & -2 \\2 & -1 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : E</b></span></p>
<br /><div>19. Coming soon 🙏🙏</div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-85668266549119838612022-10-13T10:30:00.118+08:002022-10-31T16:32:44.840+08:00Cara Membuat Tabel Distribusi Frekuensi Kumulatif dan Maknanya<p style="text-align: justify;"><span style="font-size: medium;"><b>Cara Membuat Tabel Distribusi Frekuensi Kumulatif dan Maknanya -</b> Frekuensi kumulatif adalah frekuensi yang dijumlahkan sehingg pada pembuatan tabel distribusi frekuensi kumulatif akan menjumlahkan frekuensi dari tabel distribusi frekuensi.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Distribusi Frekuensi Kumulatif dibedakan menjadi dua yaitu</span></p><p style="text-align: justify;"></p><ol><li><span style="font-size: medium;">Distribusi frekuensi kumulatif kurang dan</span></li><li><span style="font-size: medium;">Distribusi frekuensi lebih dari</span></li></ol><p></p><p style="text-align: justify;"><span style="font-size: medium;">Berikut langkah-langkah cara membuat tabel distribusi frekuensi kumulatif</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dari tabel distribusi frekuensi berikut, buatlah tabel distribusi frekuensi kumulatifnya.</span></p><div class="separator" style="clear: both; text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><span style="font-size: medium;"><img alt="Tabel distribusi frekuensi" data-original-height="304" data-original-width="283" src="https://blogger.googleusercontent.com/img/a/AVvXsEikrPARBkfziHwAq24X3iySbLtX0EFK3MTh5Gka8hJLfariFVkrKj3PomZrgFGDh-kcy6xv0kBF6ml8a6hShoUuK4xgmtSDqIaLW2-I-iCRg-J5o5QlifB_9AMj2zYNcffkQgdZi70Gn2aZKa7tPfYmzaV60ck1xewfI54xjNKl0WGCrXzzJbSv6iCm=s16000" style="margin-left: auto; margin-right: auto;" title="Tabel distribusi frekuensi" /></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://biggersplinterrattle.com/erhfawdydz?key=7aea4a66acb56030f11ced391f8ffd86" rel="nofollow" target="_blank">Tabel 1. Data Distribusi Frekuensi</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEikrPARBkfziHwAq24X3iySbLtX0EFK3MTh5Gka8hJLfariFVkrKj3PomZrgFGDh-kcy6xv0kBF6ml8a6hShoUuK4xgmtSDqIaLW2-I-iCRg-J5o5QlifB_9AMj2zYNcffkQgdZi70Gn2aZKa7tPfYmzaV60ck1xewfI54xjNKl0WGCrXzzJbSv6iCm" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"></span></a></div></div><span style="font-size: medium;"><br /></span><h2 style="text-align: justify;"><span style="font-size: medium;"><b>Membuat Tabel Distribusi Frekuensi Kumulatif Kurang Dari (<i>fk<</i>)</b></span></h2><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah</span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Tambahkan kolom Frekuensi kumulatif kurang dari (fk<) dari tabel diatas.</span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Frekuensi kumulatif kelas pertama sama dengan frekuensi kelas pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;">3. Frekuensi kumulatif kelas kedua sama dengan frekuensi kumulatif kelas pertama ditambah frekuensi kelas kedua</span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Frekuensi kumulatif kelas ketiga sama dengan frekuensi kumulatif kelas kedua ditambah frekuensi kelas ketiga</span></p><p style="text-align: justify;"><span style="font-size: medium;">5. Frekuensi kumulatif kelas keempat sama dengan frekuensi kumulatif kelas ketiga ditambah frekuensi kelas keempat</span></p><p style="text-align: justify;"><span style="font-size: medium;">6. Frekuensi kumulatif kelas kelima sama dengan frekuensi kumulatif kelas keempat ditambah frekuensi kelas kelima</span></p><p style="text-align: justify;"><span style="font-size: medium;">7. Frekuensi kumulatif kelas keenam sama dengan frekuensi kumulatif kelas kelima ditambah frekuensi kelas keenam.</span></p><p style="text-align: justify;"><span style="font-size: medium;">8. Frekuensi kumulatif kelas ketujuh sama dengan frekuensi kumulatif kelas keenam ditambah frekuensi kelas ketujuh</span></p><p style="text-align: justify;"><span style="font-size: medium;">9. Frekuensi kumulatif kelas ketujuh (kelas terakhir) harus sama dengan jumlah frekuensi</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah diatas diilustrasikan seperti gambar berikut</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEidY4qUnRU6kFHl6tcRg0zMP3zOp-bwp7hEoFuxt7KsT2cngCQROU1AgetsheOeCNeCtiTsN2m7796LSyt1pjQflbFWkF9obTYVKCaz_pOaA8bAMWnXekBDZCCu7mSWXkaxU0lEKFcUHaaQ1OoKa6qJQz0-mfuxmmaP-WYEuBeNgheuxN0ZwvAAqz3U" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Ilustrasi tabel distribusi frekuensi kumulatif kurang dari" data-original-height="298" data-original-width="408" src="https://blogger.googleusercontent.com/img/a/AVvXsEidY4qUnRU6kFHl6tcRg0zMP3zOp-bwp7hEoFuxt7KsT2cngCQROU1AgetsheOeCNeCtiTsN2m7796LSyt1pjQflbFWkF9obTYVKCaz_pOaA8bAMWnXekBDZCCu7mSWXkaxU0lEKFcUHaaQ1OoKa6qJQz0-mfuxmmaP-WYEuBeNgheuxN0ZwvAAqz3U=s16000" title="Ilustrasi tabel distribusi frekuensi kumulatif kurang dari" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://biggersplinterrattle.com/c6z20r4vgh?key=d5f8540a183d8942b0f24acb83ebdd74" target="_blank">Tabel 2. Ilustrasi membuat distribusi frekuensi kumulatif kurang dari</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"></span></div><p></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><span style="font-size: medium;">Sehingga tabel distribusi frekuensi kumulatif kurang dari adalah</span><p></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEijc4jeZiDCmRh_lxAztil52NzCVGpflIwcNTFF0IWsuoDQmtIfbq5XBlIuw9RGqeMy0RVeNx9AvVcTPwTKfaZdw__eLcBiTPrpjJmWZh1UiJcnAqTXM7gDOt6Rsgq9TN-g-dwNil5W_3sDXOxFQ9-MrAKh9FilgTFQAWuCJfihcQz9tvNFLwUMV3fM" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Tabel distribusi frekuensi kumulatif kurang dari" data-original-height="302" data-original-width="409" src="https://blogger.googleusercontent.com/img/a/AVvXsEijc4jeZiDCmRh_lxAztil52NzCVGpflIwcNTFF0IWsuoDQmtIfbq5XBlIuw9RGqeMy0RVeNx9AvVcTPwTKfaZdw__eLcBiTPrpjJmWZh1UiJcnAqTXM7gDOt6Rsgq9TN-g-dwNil5W_3sDXOxFQ9-MrAKh9FilgTFQAWuCJfihcQz9tvNFLwUMV3fM=s16000" title="Tabel distribusi frekuensi kumulatif kurang dari" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://biggersplinterrattle.com/c6z20r4vgh?key=d5f8540a183d8942b0f24acb83ebdd74" target="_blank">Tabel 3. Distribusi frekuensi kumulatif kurang dari</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"></span></div><p></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><h2><span style="font-size: medium;">Makna Frekuensi Kumulatif Kurang Dari</span></h2><p></p><p style="text-align: justify;"><span style="font-size: medium;">Makna/arti dari frekuensi kumulatif kurang dari adalah untuk membaca banyak data yang kurang dari berdasarkan tepi atas kelas</span></p><p style="text-align: justify;"></p><ol><li><span style="font-size: medium;"><i>fk<</i> sama dengan 5 artinya banyak data yang kurang dari 49,5 adalah 5</span></li><li><span style="font-size: medium;"><i>fk<</i> sama dengan 15 artinya banyak data yang kurang dari 54,5 adalah 15</span></li><li><span style="font-size: medium;"><i>fk<</i> sama dengan 23 artinya banyak data yang kurang dari 59,5 adalah 23</span></li><li><span style="font-size: medium;"><i>fk<</i><span> sama dengan 35 artinya banyak data yang kurang dari 64,5 adalah 35</span></span></li><li><span style="font-size: medium;"><i>fk<</i><span> sama dengan 41 artinya banyak data yang kurang dari 69,5 adalah 41</span></span></li><li><span style="font-size: medium;"><i>fk<</i><span> sama dengan 45 artinya banyak data yang kurang dari 74,5 adalah 45</span></span></li><li><span style="font-size: medium;"><i>fk<</i><span> sama dengan 50 artinya banyak data yang kurang dari 79,5 adalah 50</span></span></li></ol><span style="font-size: medium;"><br /></span><p></p><h2 style="text-align: left;"><b style="text-align: justify;"><span style="font-size: medium;">Membuat Tabel Distribusi Frekuensi Kumulatif Lebih Dari (<i>fk></i>)</span></b></h2><div><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah</span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Tambahkan kolom Frekuensi kumulatif lebih dari (<i>fk></i>) dari tabel diatas.</span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Frekuensi kumulatif kelas pertama sama dengan jumlah frekuensi dari tabel diatas</span></p><p style="text-align: justify;"><span style="font-size: medium;">3. Frekuensi kumulatif kelas kedua sama dengan frekuensi kumulatif kelas pertama dikurangi frekuensi kelas pertama</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>4. </span>Frekuensi kumulatif kelas ketiga sama dengan frekuensi kumulatif kelas kedua dikurangi frekuensi kelas kedua</span></p><p style="text-align: justify;"><span style="font-size: medium;">5. Frekuensi kumulatif kelas keempat sama dengan frekuensi kumulatif kelas ketiga dikurangi frekuensi kelas ketiga.</span></p><p style="text-align: justify;"><span style="font-size: medium;">6. Frekuensi kumulatif kelas kelima sama dengan frekuensi kumulatif kelas keempat dikurangi frekuensi kelas keempat</span></p><p style="text-align: justify;"><span style="font-size: medium;">7. Frekuensi kumulatif kelas keenam sama dengan frekuensi kumulatif kelas kelima dikurangi frekuensi kelas kelima</span></p><p style="text-align: justify;"><span style="font-size: medium;">8. Frekuensi kumulatif kelas ketujuh sama dengan frekuensi kumulatif kelas keenam dikurangi frekuensi kelas keenam</span></p><p style="text-align: justify;"><span style="font-size: medium;">9. Frekuensi kumulatif kelas ketujuh (kelas terakhir) harus sama denga frekuensi kelas ketujuh (kelas terakhir)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah diatas diilustrasikan seperti gambar berikut</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiZswQB6HyAoHSZL-HEL5s1gcAFluLAbmGuCmohMgM8tqQUvlbgJUgYzYY3XKRbCxyXhFq3GsLpyw4zHjixrgyzdP4EA9Cm7rayK4fWEhnxxQd2V5JOG0SG3qAOpwhglgp5NfhDH3IRYHpt_1atwq9t7kYd67fqoSQ0v7nPS8VQYfCcGtxvTvn8_qIa" style="margin-left: auto; margin-right: auto;"><img alt="Ilustrasi tabel distibusi frekuensi kumulatif lebih dari" data-original-height="305" data-original-width="422" src="https://blogger.googleusercontent.com/img/a/AVvXsEiZswQB6HyAoHSZL-HEL5s1gcAFluLAbmGuCmohMgM8tqQUvlbgJUgYzYY3XKRbCxyXhFq3GsLpyw4zHjixrgyzdP4EA9Cm7rayK4fWEhnxxQd2V5JOG0SG3qAOpwhglgp5NfhDH3IRYHpt_1atwq9t7kYd67fqoSQ0v7nPS8VQYfCcGtxvTvn8_qIa=s16000" title="Ilustrasi tabel distibusi frekuensi kumulatif lebih dari" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://biggersplinterrattle.com/c6z20r4vgh?key=d5f8540a183d8942b0f24acb83ebdd74" target="_blank">Tabel 4. Ilustrasi membuat distribusi frekuensi kumulatif lebih dari</a></td></tr></tbody></table><span style="font-size: medium;"><br /><span style="text-align: left;">Sehingga tabel distribusi frekuensi kumulatif lebih dari adalah</span></span><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhG89YxPn6iSk-jjob1upRMSW4yuVOW_dl_-wt7myIsoAfK1b4tpfL8HSZn2TeTY7jpGDORrrPtFHI_3fn_Ad9DwUQ59hXUY0ti4ck0yiZU5cZcXGMFHmIXtTHjVsl_yCSRj0kJmF3utz_gth2sKUwTOBtaFa3tQsL6yQzIMlqcpP8EHrwMoeU_hPJy" style="margin-left: auto; margin-right: auto;"><img alt="Tabel distribusi frekuensi kumulatif lebih dari" data-original-height="301" data-original-width="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEhG89YxPn6iSk-jjob1upRMSW4yuVOW_dl_-wt7myIsoAfK1b4tpfL8HSZn2TeTY7jpGDORrrPtFHI_3fn_Ad9DwUQ59hXUY0ti4ck0yiZU5cZcXGMFHmIXtTHjVsl_yCSRj0kJmF3utz_gth2sKUwTOBtaFa3tQsL6yQzIMlqcpP8EHrwMoeU_hPJy=s16000" title="Tabel distribusi frekuensi kumulatif lebih dari" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://biggersplinterrattle.com/erhfawdydz?key=7aea4a66acb56030f11ced391f8ffd86" target="_blank">Tabel 5. Distribusi frekuensi kumulatif lebih dari</a></td></tr></tbody></table><span style="font-size: medium;"><span style="text-align: left;"><br /></span></span><h2 style="text-align: left;"><span style="font-size: medium;">Makna Frekuensi Kumulatif Lebih Dari</span></h2></div><div><span style="font-size: medium;">Makna/arti dari frekuensi kumulatif lebih dari adalah untuk membaca banyak data yang lebih dari berdasarkan tepi bawah kelas</span><p></p><ol><li><span style="font-size: medium;"><i>fk></i> sama dengan 50 artinya banyak data yang lebih dari dari 44,5 adalah 50</span></li><li><span style="font-size: medium;"><i>fk></i> sama dengan 45 artinya banyak data yang lebih dari dari 49,5 adalah 45</span></li><li><span style="font-size: medium;"><i>fk></i> sama dengan 35 artinya banyak data yang lebih dari dari 54,5 adalah 35</span></li><li><span style="font-size: medium;"><i>fk></i> sama dengan 27 artinya banyak data yang lebih dari dari 59,5 adalah 27</span></li><li><span style="font-size: medium;"><i>fk></i> sama dengan 15 artinya banyak data yang lebih dari dari 64,5 adalah 15</span></li><li><span style="font-size: medium;"><i>fk></i> sama dengan 9 artinya banyak data yang lebih dari dari 69,5 adalah 9</span></li><li><span style="font-size: medium;"><i>fk></i> sama dengan 5 artinya banyak data yang lebih dari dari 74,5 adalah 5</span></li></ol><span style="font-size: medium;"><div style="text-align: justify;">Jika kedua tabel distribusi frekuensi kumulatif kurang dan kurang dari digabung akan seperti tabel berikut</div><div style="text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEij8Rlg8QkuTqU5P4ygYr0T4gQSOMq6-On8MHOR7UakF7436UYJkxnl-_XnCmUYmsnxhdKKV_o6rXozTopM_QId9r7IsGJs-hfIDBmpdeBJlwlmQeYRy-HIjaLmehYtG534BAdrFHpHLJKj4aGivEWma-1WrXy2eCtyAwilkg7PQl4quSY4sn65w59P" style="margin-left: auto; margin-right: auto;"><img alt="Tabel distribusi frekuensi kumulatif" data-original-height="314" data-original-width="501" src="https://blogger.googleusercontent.com/img/a/AVvXsEij8Rlg8QkuTqU5P4ygYr0T4gQSOMq6-On8MHOR7UakF7436UYJkxnl-_XnCmUYmsnxhdKKV_o6rXozTopM_QId9r7IsGJs-hfIDBmpdeBJlwlmQeYRy-HIjaLmehYtG534BAdrFHpHLJKj4aGivEWma-1WrXy2eCtyAwilkg7PQl4quSY4sn65w59P=s16000" title="Tabel distribusi frekuensi kumulatif" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://biggersplinterrattle.com/erhfawdydz?key=7aea4a66acb56030f11ced391f8ffd86" target="_blank">Tabel 6. Distrubusi frekuensi kumulatif</a></td></tr></tbody></table><br />Demikian cara membuat tabel distribusi frekuensi kumulatif dan maknanya, semoga pembahasan ini bermanfaat.</div></span></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-44116721135134746972022-10-11T18:23:00.029+08:002022-10-31T17:16:10.480+08:00Pembahasan Soal Barisan dan Deret Aritmatika Kelas X Fase E Kurikulum Merdeka<p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b></b></span></span></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><span style="text-align: left;"><span><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi27nJIOi9zxvqCtRLhk6ixsLbX9zHO8PG94hkp3Efebn1YmgMhNG9iDR8T2amrofEfcyJ_h2zzf1OeIyyOBEwuf16HkUNDvlItgmA_rwLhMLO4GUCjcGhz-Dnd6Gabf7hPv1eGHmLswd1JaKFg0wM_VDDDabaxX8R3pdFdafk41XFo4Fk-YARiZKm2/s1280/BARISAN.PNG" style="margin-left: 1em; margin-right: 1em;"><img alt="Barisan dan deret aritmatika Fase E Kurikulum Merdeka" border="0" data-original-height="720" data-original-width="1280" height="113" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi27nJIOi9zxvqCtRLhk6ixsLbX9zHO8PG94hkp3Efebn1YmgMhNG9iDR8T2amrofEfcyJ_h2zzf1OeIyyOBEwuf16HkUNDvlItgmA_rwLhMLO4GUCjcGhz-Dnd6Gabf7hPv1eGHmLswd1JaKFg0wM_VDDDabaxX8R3pdFdafk41XFo4Fk-YARiZKm2/w200-h113/BARISAN.PNG" style="float: left; margin: 5px 9px;" title="Barisan dan deret aritmatika Fase E Kurikulum Merdeka" width="200" /></a></b></span></span></span></div><span style="font-size: medium;"><div style="text-align: justify;"><span><span><b>Pembahasan Soal Barisan dan Deret Aritmatika Kelas X Fase E SMA/MA Kurikulum Merdeka - </b></span></span><span>Barisan dan Deret Aritmatika merupakan salah satu materi modul kelas X atau Fase E SMA/MA yang mengimplementasikan Kurikulum Merdeka Belajar. Untuk membantu pemahaman konsep pada modul barisan dan deret aritmatika bisa mempelajarinya melalui link <a href="https://www.sambimatika.my.id/2021/10/barisan-dan-deret-aritmatika-materi-dan.html" rel="nofollow" target="_blank">https://www.sambimatika.my.id/2021/10/barisan-dan-deret-aritmatika-materi-dan.html</a>. Pada postingan ini hanya membahas soal-soal pada materi barisan dan deret aritmatika sebagai berikut.</span></div><h2 style="text-align: justify;"><span style="font-size: medium;">SOAL-SOAL BARISAN DAN DERET ARITMATIKA SERTA PEMBAHASANNYA</span></h2></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">1. Dari barisan 3, 5, 7, 9, 11, ... suku ke 21 adalah....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 40</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 43</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 46</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 49</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 5</span></p><p style="text-align: justify;"><b><span style="font-size: medium;">Pembahasan</span></b></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : a = 3, b = 5 - 3 = 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : U21 = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">U21 = a + 20b</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span>= 3 + 20 . 2</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span>= 3 + 40</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span>= 43</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">2. Suatu barisan aritmatika diketahui suku ke 4 adalah 6 dan beda 3. Suku ke 8 adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 18</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 31</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 34</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 37</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 40</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : U4 = 6, b = 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : U8</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">U4 = a + 3b</span></p><p style="text-align: justify;"><span style="font-size: medium;">6 = a + 3.3</span></p><p style="text-align: justify;"><span style="font-size: medium;">6 = a + 9</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 6 - 9</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = -3</span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">U8 = a + 7b</span></p><p style="text-align: justify;"><span style="font-size: medium;">= -3 + 7 . 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">= -3 + 21</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 18</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">3. Suatu barisan aritmatika diketahui suku ke 15 adalah 30 dan bedanya -5. Suku ke 6 adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 65</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 25</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 75</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 80</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 90</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : U15 = 30, b = -5</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : U6 =.....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">U15 = a + 14b</span></p><p style="text-align: justify;"><span style="font-size: medium;">30 = a + 14 (-5)</span></p><p style="text-align: justify;"><span style="font-size: medium;">30 = a + (-60)</span></p><p style="text-align: justify;"><span style="font-size: medium;">30 = a - 60</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 30 + 60</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 90</span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">U6 = a + 5b</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 90 + 5(-5)</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 90 - 15</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 75</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Rumus suku ke n dari barisan aritmatika 4, 9, 14, 19, 24, ... adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 5n + 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 5n - 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">C 5n + 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 5n - 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 5n + 3</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : a = 4, b = 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : Un</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jawab</span></p><p style="text-align: justify;"><span style="font-size: medium;">Un = a + (n - 1)b</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 4 + (n - 1)5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 4 + 5n - 5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 5n + 4 - 5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 5n - 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">5. Suatu barisan aritmatika diketahui suku ke 6 adalah -4 dan suku ke 9 adalah -19, maka suku ke 11 adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. -34</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. -29</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. -19</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. -24</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. -14</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : U6 = -4, U9 = -19</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : U11 = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">U6 = a + 5b</span></p><p style="text-align: justify;"><span style="font-size: medium;">-4 = a + 5b</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 5b = -4 ..........(1)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">U9 = a + 8b</span></p><p style="text-align: justify;"><span style="font-size: medium;">-19 = a + 8b</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 8b = -19 .....(2)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Eliminasi varabel a dari persamaan (1) dan (2)</span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}a+5b=\,&space;\,&space;-4\,&space;\,&space;\,&space;\,\,&space;&space;&space;\\\underline{a+8b=-19&space;}\,&space;-&space;\\-3b=15\\b=\frac{15}{-3}\\b=-5\end{matrix}" title="https://latex.codecogs.com/svg.image?\begin{matrix}a+5b=\, \, -4\, \, \, \,\, \\\underline{a+8b=-19 }\, - \\-3b=15\\b=\frac{15}{-3}\\b=-5\end{matrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Subtitusi b = -5 ke persamaan (1)</span></p><p style="text-align: left;"><span style="font-size: medium;">a + 5b = -4</span></p><p style="text-align: left;"><span style="font-size: medium;">a + 5(-5) = -4</span></p><p style="text-align: left;"><span style="font-size: medium;">a - 25 = -4</span></p><p style="text-align: left;"><span style="font-size: medium;">a = -4 + 25</span></p><p style="text-align: left;"><span style="font-size: medium;">a = 21</span></p><p style="text-align: left;"><span style="font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;">U11 = a + 10b</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span>= 21 + 10(-5)</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span>= 21 - 50</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span>= -29</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">6. Hasil dari 5 + 7 + 9 + 11 + ... + 41 adalah .....</span></p><p style="text-align: left;"><span style="font-size: medium;">A. 379</span></p><p style="text-align: left;"><span style="font-size: medium;">B. 437</span></p><p style="text-align: left;"><span style="font-size: medium;">C. 471</span></p><p style="text-align: left;"><span style="font-size: medium;">D. 407</span></p><p style="text-align: left;"><span style="font-size: medium;">E. 207</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;">Dik : a = 5, b = 7 - 5 = 2 dan Un = 41</span></p><p style="text-align: left;"><span style="font-size: medium;">Dit : Sn = ....?</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: left;"><span style="font-size: medium;">Un = 41</span></p><p style="text-align: left;"><span style="font-size: medium;">a + (n - 1)b = 41</span></p><p style="text-align: left;"><span style="font-size: medium;">5 + (n - 1)2 = 41</span></p><p style="text-align: left;"><span style="font-size: medium;">5 + 2n - 2 = 41</span></p><p style="text-align: left;"><span style="font-size: medium;">2n + 3 = 41</span></p><p style="text-align: left;"><span style="font-size: medium;">2n = 41 - 3</span></p><p style="text-align: left;"><span style="font-size: medium;">2n = 38</span></p><p style="text-align: left;"><span style="font-size: medium;">n = 38/2</span></p><p style="text-align: left;"><span style="font-size: medium;">n = 19</span></p><p style="text-align: left;"><span style="font-size: medium;">maka U19 = 41</span></p><p style="text-align: left;"><span style="font-size: medium;">Sehingga diperoleh</span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;a+Un&space;\right&space;)" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( a+Un \right )" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{19}=\frac{19}{2}\left&space;(&space;5+U_{19}&space;\right&space;)" title="https://latex.codecogs.com/svg.image?S_{19}=\frac{19}{2}\left ( 5+U_{19} \right )" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{19}{2}\left&space;(&space;5+41&space;\right&space;)" title="https://latex.codecogs.com/svg.image?=\frac{19}{2}\left ( 5+41 \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{19}{2}\left&space;(&space;46&space;\right&space;)" title="https://latex.codecogs.com/svg.image?=\frac{19}{2}\left ( 46 \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=19.23=437" title="https://latex.codecogs.com/svg.image?=19.23=437" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : B</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">7. Jika 4 + 6 + 8 + 10 + ... + x = 130, maka nilai x adalah ....</span></p><p style="text-align: left;"><span style="font-size: medium;">A. 10</span></p><p style="text-align: left;"><span style="font-size: medium;">B. 15</span></p><p style="text-align: left;"><span style="font-size: medium;">C. 18</span></p><p style="text-align: left;"><span style="font-size: medium;">D. 22</span></p><p style="text-align: left;"><span style="font-size: medium;">E. 32</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;">Dik : a = 4, b = 6 - 2 = 2, Un = x dan Sn = 130</span></p><p style="text-align: left;"><span style="font-size: medium;">Dit : x = ....?</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Jawab</b></span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;2a+(n-1)b&space;\right&space;)" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( 2a+(n-1)b \right )" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?130=\frac{n}{2}\left&space;(&space;2.4+(n-1)2&space;\right&space;)" title="https://latex.codecogs.com/svg.image?130=\frac{n}{2}\left ( 2.4+(n-1)2 \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?130=\frac{n}{2}\left&space;(&space;8+2n-2&space;\right&space;)" title="https://latex.codecogs.com/svg.image?130=\frac{n}{2}\left ( 8+2n-2 \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?130=\frac{n}{2}\left&space;(&space;6+2n&space;\right&space;)" title="https://latex.codecogs.com/svg.image?130=\frac{n}{2}\left ( 6+2n \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?130=n\left&space;(&space;3+n&space;\right&space;)" title="https://latex.codecogs.com/svg.image?130=n\left ( 3+n \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?130=3n+n^{2}" title="https://latex.codecogs.com/svg.image?130=3n+n^{2}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?n^{2}+3n-130=0" title="https://latex.codecogs.com/svg.image?n^{2}+3n-130=0" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?(n+13)(n-10)=0" title="https://latex.codecogs.com/svg.image?(n+13)(n-10)=0" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?(n+13)=0\,&space;\,&space;\textrm{atau}\,&space;\,&space;(n-10)=0" title="https://latex.codecogs.com/svg.image?(n+13)=0\, \, \textrm{atau}\, \, (n-10)=0" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?n=-13\,&space;\,&space;(TM)\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;\,&space;n=10" title="https://latex.codecogs.com/svg.image?n=-13\, \, (TM)\, \, \, \, \, \, \, \, \, n=10" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Karena n = 10 maka U10 = x</span></p><p style="text-align: left;"><span style="font-size: medium;">U10 = x</span></p><p style="text-align: left;"><span style="font-size: medium;">a + 9b = x</span></p><p style="text-align: left;"><span style="font-size: medium;">4 + 9.2 = x</span></p><p style="text-align: left;"><span style="font-size: medium;">4 + 18 = x</span></p><p style="text-align: left;"><span style="font-size: medium;">22 = x</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci Jawaban : D</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">8. Suku keempat dari dari suatu barisan aritmatika adalah 20 dan jumlah lima suku pertamanya sama dengan 80. Jumlah sebelas suku pertamanya adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 196</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 210</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 264</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 308</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 332</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : U4 = 20, S5 = 80</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : S11 = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">U4 = 20</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 3b = 20 ..........(1)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{n}=\frac{n}{2}\left&space;(&space;2a+(n-1)b&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{n}=\frac{n}{2}\left ( 2a+(n-1)b \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?S_{5}=\frac{5}{2}\left&space;(&space;2a+(5-1)b&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{5}=\frac{5}{2}\left ( 2a+(5-1)b \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?80=\frac{5}{2}\left&space;(&space;2a+4b&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?80=\frac{5}{2}\left ( 2a+4b \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?80=5\left&space;(&space;a+2b&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?80=5\left ( a+2b \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?80=5a+10b" style="text-align: left;" title="https://latex.codecogs.com/svg.image?80=5a+10b" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?16=a+2b" style="text-align: left;" title="https://latex.codecogs.com/svg.image?16=a+2b" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?a+2b=16" style="text-align: left;" title="https://latex.codecogs.com/svg.image?a+2b=16" /> ..........(2)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Eliminasi a dari persamaan (1) dan (2)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}a+3b=20&space;\\\underline{a+2b=16}-\\b&space;=&space;4\end{matrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{matrix}a+3b=20 \\\underline{a+2b=16}-\\b = 4\end{matrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Substitusi b = 4 ke persamaan (1)</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 3b = 20</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 3.4 = 20</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 12 = 20</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 20 - 12</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 8</span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{n}=\frac{n}{2}\left&space;(&space;2a+(n-1)b&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{n}=\frac{n}{2}\left ( 2a+(n-1)b \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left&space;(&space;2.8+(11-1)4&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left ( 2.8+(11-1)4 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left&space;(&space;16+(10)4&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left ( 16+(10)4 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left&space;(&space;16+40&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left ( 16+40 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left&space;(&space;56&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{11}=\frac{11}{2}\left ( 56 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?S_{11}=11(28)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{11}=11(28)" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?S_{11}=308" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{11}=308" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>9. Dari suatu deret aritmatika diketahui jumlah n suku pertamanya ditentukan dengan rumus </span><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;3n+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( 3n+5 \right )" /> . Suku ke 6 adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 19</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 33</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 36</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 39</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 42</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : <img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;3n+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( 3n+5 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : U6 = ......?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil n = 6, maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;3n+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( 3n+5 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{6}=\frac{6}{2}\left&space;(&space;3.6+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{6}=\frac{6}{2}\left ( 3.6+5 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=3\left&space;(&space;18+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=3\left ( 18+5 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=3\left&space;(&space;23&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=3\left ( 23 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=69" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=69" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>Ambil n = 5, maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;3n+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( 3n+5 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{5}=\frac{5}{2}\left&space;(&space;3.5+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{5}=\frac{5}{2}\left ( 3.5+5 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{5}{2}\left&space;(&space;15+5&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{5}{2}\left ( 15+5 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{5}{2}\left&space;(&space;20&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{5}{2}\left ( 20 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=5(10)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=5(10)" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=50" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=50" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sementara</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?S_{6}=S_{5}+U_{6}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{6}=S_{5}+U_{6}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?69=50+U_{6}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?69=50+U_{6}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?U_{6}=69-50=19" style="text-align: left;" title="https://latex.codecogs.com/svg.image?U_{6}=69-50=19" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">10. Jumlah bilangan bulat antara 10 dan 60 yang habis dibagi 3 adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 552</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 486</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 462</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 312</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 396</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Deret artimatika dari bilangan antara 10 dan 60 yang habis dibagi 3 adalah</span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + 15 + 18 + 21 + ... + 57</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dari deret aritamatika diatas :</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : a = 12, b = 3 dan Un = 57</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : Sn = .... ?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Un = 57</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + (n - 1)b = 57</span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + (n - 1)3 = 57</span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + 3n - 3 = 57</span></p><p style="text-align: justify;"><span style="font-size: medium;">3n + 9 = 57</span></p><p style="text-align: justify;"><span style="font-size: medium;">3n = 57 - 9</span></p><p style="text-align: justify;"><span style="font-size: medium;">3n = 48</span></p><p style="text-align: justify;"><span style="font-size: medium;">n = 48/3</span></p><p style="text-align: justify;"><span style="font-size: medium;">n = 16</span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena n = 16 maka U16 = 57 sehingga yang akan dicari adalah S16.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;a+Un&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( a+Un \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{16}=\frac{16}{2}\left&space;(&space;a+U_{16}&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{16}=\frac{16}{2}\left ( a+U_{16} \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=8\left&space;(&space;12+57&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=8\left ( 12+57 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=8\left&space;(&space;69&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=8\left ( 69 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=552" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=552" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;">11. Dalam suatu barisan aritmatika jumlah suku keempat dan keenam adalah 28. Jika suku kedua barisan itu adalah 5, suku ke sembilan adalah .....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 19</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 21</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 24</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 26</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 28</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : U4 + U6 = 28, U2 = 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dit : U9 = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawab</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">U4 + U6 = 28</span></p><p style="text-align: justify;"><span style="font-size: medium;">(a + 3b) + (a + 5b) = 28</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + a + 3b + 5b = 28</span></p><p style="text-align: justify;"><span style="font-size: medium;">2a + 8b = 28 ........ (1)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">U2 = 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + b = 5 ........(2)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ubah persamaan (2) menjadi a =</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + b = 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 5 - b ......(3)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi persamaan (3) ke persamaan (1)</span></p><p style="text-align: justify;"><span style="font-size: medium;">2a + 8b = 28</span></p><p style="text-align: justify;"><span style="font-size: medium;">2(5 - b) + 8b = 28</span></p><p style="text-align: justify;"><span style="font-size: medium;">10 - 2b + 8b = 28</span></p><p style="text-align: justify;"><span style="font-size: medium;">10 + 6b = 28</span></p><p style="text-align: justify;"><span style="font-size: medium;">6b = 28 - 10</span></p><p style="text-align: justify;"><span style="font-size: medium;">6b = 18</span></p><p style="text-align: justify;"><span style="font-size: medium;">b = 18/6 = 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi b = 3 ke persamaan (3)</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 5 - b</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 5 - 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">U9 = a + 8b</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 2 + 8.3</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 2 + 24</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 26</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">12. Jumlah semua bilangan ganjil antara 300 dan 750 yang bukan kelipatan 7 adalah .....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 84.000</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 84.215</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 84.250</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 84.375</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 84.500</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Deret bilangan ganjil antara 300 dan 750 adalah</span></p><p style="text-align: justify;"><span style="font-size: medium;">301 + (303 + 305 + 307 + 309 + 311 + 313) + 315 + (317 + 319 + 321 + 323+ 325 + 327 ) + 329 + ....+ 735 + (737 +739 + 741 + 743 + 745 + 747) + 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">Misalkan deret diatas adalah Sx</span></p><p style="text-align: justify;"><span style="font-size: medium;">Perhatikan deret aritmatika diatas yang didalam kurung merupakan bilangan ganjil yang bukan kelipatan 7 dan yang tidak didalam kurung merupakan bilangan ganjil yang merupakan kelipatan 7</span></p><p style="text-align: justify;"><span style="font-size: medium;">Bilangan ganjil yang merupakan kelipan 7 membentuk sebuah deret aritmatika yaitu</span></p><p style="text-align: justify;"><span style="font-size: medium;">301 + 315 + 329 + ... + 749 dan memiliki beda 14.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jumlah bilangan ganjil antara 300 dan 750 yang bukan kelipatan 7 = S</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jumlah bilangan ganjil antara 300 dan 750 = Sx</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jumlah bilangan ganjil antara 300 dan 750 yang merupakan kelipatan 7 = Sy</span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jumlah bilangan ganjil antara 300 dan 750 bukan kelipatan 7 = Jumlah bilangan ganjil antara 300 dan 750 - Jumlah bilangan ganjil antara 300 dan 750 kelipatan 7</span></p><p style="text-align: justify;"><span style="font-size: medium;">S = Sx - Sy</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Untuk deret aritmatika Sx</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">301 + (303 + 305 + 307 + 309 + 311 + 313) + 315 + (317 + 319 + 321 + 323+ 325 + 327 ) + 329 + .... + (... + 747) + 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : a = 301 , b = 303 - 301 = 2 dan Un = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil Un = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">Un = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + (n -1)b = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">301 + (n - 1)2 = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1)2 = 749 - 301</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1) 2 = 448</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 448/2</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 224</span></p><p style="text-align: justify;"><span style="font-size: medium;">n = 224 + 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">n = 225</span></p><p style="text-align: justify;"><span style="font-size: medium;">sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;a+Un&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( a+Un \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{225}=\frac{225}{2}\left&space;(&space;301+U_{225}&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{225}=\frac{225}{2}\left ( 301+U_{225} \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{225}{2}\left&space;(&space;301+749&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{225}{2}\left ( 301+749 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{225}{2}\left&space;(&space;1.050&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{225}{2}\left ( 1.050 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=225.525=118.125" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=225.525=118.125" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi Sx = 118.125</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Untuk deret aritmatika Sy</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">301 + 315 + 329 + ... + 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : a = 301, b = 315 - 301 = 14 dan Un = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil Un = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">Un = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + (n - 1)b = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">301 + (n - 1)14 = 749</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1)14 = 749 - 301</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1)14 = 448</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 448/14</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 32</span></p><p style="text-align: justify;"><span style="font-size: medium;">n = 32 + 1 = 33</span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena n = 33 maka U33 = 749 dan akan dicari S33</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;a+Un&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( a+Un \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{33}=\frac{33}{2}\left&space;(&space;a+U_{33}&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{33}=\frac{33}{2}\left ( a+U_{33} \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{33}{2}\left&space;(&space;301+749&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{33}{2}\left ( 301+749 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{33}{2}\left&space;(&space;1.050&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{33}{2}\left ( 1.050 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=33.525=17.325" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=33.525=17.325" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi Sy = 17.325</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga</span></p><p style="text-align: justify;"><span style="font-size: medium;">S = Sx - Sy</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><span> </span>= </span><span>118.125 - 17.325</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 100.800</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : tidak ada yang benar</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">13. Jumlah semua bilangan asli dari 10 sampai 99 yang habis dibagi 3 tetapi tidak habis dibagi 4 adalah.....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 477</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 585</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 1.178</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 1.233</span></p><p style="text-align: justify;"><span style="font-size: medium;">E. 1.428</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Deret Bilangan Asli dari 10 sampai 99 yang habis dibagi 3 adalah</span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + (15 + 18 + 21) + 24 + (27 + 30 + 33) + 36 + ... 84 + (87 + 90 + 93) + 96 + ( 99)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Perhatikan bilangan yang tidak didalam kurung merupakan bilangan yang habis dibagi 3 dan habis dibagi 4, sementara bilangan yang didalam kurung adalah bilangan yang habis dibagi 3 dan tidak habis dibagi 4.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Bilangan yang habis dibagi 3 dan habis dibagi 4 membentuk deret aritmatika berikut</span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + 24 + 36 + ... + 84 + 96</span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal </span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Jumlah bilangan </span><span>Asli dari 10 sampai 99 yang habis dibagi 3 dan tidak habis dibagi 4 = S</span></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jumlah Bilangan Asli dari 10 sampai 99 yang habis dibagi 3 = Sx</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jumlah bilangan Asli dari 10 sampai 99 yang habus dibagi 3 dan habis dibagi 4 = Sy</span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><span>Jumlah bilangan </span><span>Asli dari 10 sampai 99 yang habis dibagi 3 dan tidak habis dibagi 4 = </span></span><span>Jumlah Bilangan Asli dari 10 sampai 99 yang habis dibagi 3 = Sx - </span><span>Jumlah bilangan Asli dari 10 sampai 99 yang habus dibagi 3 dan habis dibagi 4 = Sy</span></span></p><p style="text-align: justify;"><span style="font-size: medium;">S = Sx - Sy</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Untuk deret aritmatika Sx</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + (15 + 18 + 21) + 24 + (27 + 30 + 33) + 36 + ... 84 + (87 + 90 + 93) + 96 + ( 99)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahi a = 12, b = 15 - 12 = 3 dan Un = 99</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil Un = 99</span></p><p style="text-align: justify;"><span style="font-size: medium;">Un = 99</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + (n - 1)b = 99</span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + (n - 1)3 = 99</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1)3 = 99 - 12</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1)3 = 87</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 87/3</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 29</span></p><p style="text-align: justify;"><span style="font-size: medium;">n = 29 + 1 = 30</span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena n = 30 maka U30 = 99 dan akan dicari S30</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;a+Un&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( a+Un \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{30}=\frac{30}{2}\left&space;(&space;a+U_{30}&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{30}=\frac{30}{2}\left ( a+U_{30} \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{30}{2}\left&space;(&space;12+99&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{30}{2}\left ( 12+99 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=15.111=1.665" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=15.111=1.665" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka Sx = 1.665</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Untuk deret aritmatika Sy</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + 24 + 36 + ... + 84 + 96</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dik : a = 12, b = 24 - 12 = 12 dan Un = 96</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil Un = 96</span></p><p style="text-align: justify;"><span style="font-size: medium;">Un = 96</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + (n - 1)b = 96</span></p><p style="text-align: justify;"><span style="font-size: medium;">12 + (n - 1)12 = 96</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1)12 = 96 - 12</span></p><p style="text-align: justify;"><span style="font-size: medium;">(n - 1)12 = 84</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 84/12</span></p><p style="text-align: justify;"><span style="font-size: medium;">n - 1 = 7</span></p><p style="text-align: justify;"><span style="font-size: medium;">n = 7 + 1 = 8</span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena n = 8 mak U8 = 96 dan akan dicari S8</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left&space;(&space;a+Un&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?Sn=\frac{n}{2}\left ( a+Un \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?S_{8}=\frac{8}{2}\left&space;(&space;12+U_{8}&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?S_{8}=\frac{8}{2}\left ( 12+U_{8} \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{8}{2}\left&space;(&space;12+96&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{8}{2}\left ( 12+96 \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=4.108=432" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=4.108=432" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka Sy = 432</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi</span></p><p style="text-align: justify;"><span style="font-size: medium;">S = Sx - Sy</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><span> </span>= </span><span>1.665 - 432 = 1.233</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci Jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">14. Diketahui barisan aritmatika -8, -5, -2, ..., 73 Tentukan banyak suku barisan tersebut</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dik : a = -8</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"> b = -5 - (-8) = -5 + 8 = 3</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"> Un = 73</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dit : n = ....?</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Un = a + (n - 1)b</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">73 = -8 + (n - 1) 3</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">73 = -8 + 3n - 3</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">73 = -11 + 3n</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">3n = 73 + 11</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">3n = 84</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">n = 84/3</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">n = 28</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Jadi banyak suku dari barisan tersebut adalah 28</span></span></p><div><span style="font-size: medium;"><span style="text-align: left;"><br /></span></span></div><div><span style="font-size: medium;"><span style="text-align: left;"><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>15. Diketahui barisan aritmarika dengan hasil penjumlahan suku ke-3 dan suku ke-5 adalah 68 dan hasil penjumlahan suku ke-6 dan suku ke-8 adalah 44. Tentukan suku ke-28 barisan tersebut.</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>Dik : U3 + U5 = 68</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span> U6 + U8 = 44</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>Dit : U28 = ....?</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>Jawab</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>U3 + U5 = 68</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>(a + 2b) + (a + 4b) = 68</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>2a + 6b = 68 (kedua ruas sama-sama dibagi 2)</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>a + 3b = 34 ......... (1)</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><br /></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>U6 + U8 = 44</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>(a + 5b) + (a + 7b) = 44</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>2a + 12b = 44 (kedua ruas sama-sama dibagi 2)</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span>a + 6b = 22 ........... (2)</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><br /></span></span></span></p><p><span style="font-size: medium;">Eliminasi a dari persamaan (1) dan (2)</span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}a+3b=34\,&space;\,&space;\,&space;\,&space;\,&space;\\\underline{a+6b=22}-\\-3b=12\\b=\frac{12}{-3}\\b=-4\end{matrix}" title="https://latex.codecogs.com/svg.image?\begin{matrix}a+3b=34\, \, \, \, \, \\\underline{a+6b=22}-\\-3b=12\\b=\frac{12}{-3}\\b=-4\end{matrix}" /></span></p><p><span style="font-size: medium;">Subtitusi b = -4 ke persamaan (1)</span></p><p><span style="font-size: medium;">a + 3b = 34</span></p><p><span style="font-size: medium;">a + 3(-4) = 34</span></p><p><span style="font-size: medium;">a - 12 = 34</span></p><p><span style="font-size: medium;">a = 34 + 12</span></p><p><span style="font-size: medium;">a = 46</span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">Sehingga diperoleh</span></p><p><span style="font-size: medium;">U28 = a + 27b</span></p><p><span style="font-size: medium;"><span> </span><span> </span>= 46 + 27(-4)</span></p><p><span style="font-size: medium;"><span> </span><span> </span>= 46 - 108</span></p><p><span style="font-size: medium;"><span> </span><span> </span>= -62</span></p><p><span style="font-size: medium;">Jadi besar suku ke-28 adalah -62</span></p></span></span></div><p style="text-align: justify;"><span style="font-size: medium;"><span><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">16. Diketahui barisan aritmatika dengan suku ke-2 adalah 17. Jika hasil penjumlahan suku ke-5, suku ke-7, dan suku ke-10 adalah -13. Tentukan beda barisan dan suku ke-6 barisan tersebut</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dik : U2 = 17</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">U5 + U7 + U10 = -13</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dit : b = ....? dan</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">U6 = .....?</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Jawab</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">U2 = 17</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">a + b = 17 ........ (1)</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">U5 + U7 + U10 = -13</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">(a + 4b) + (a + 6b) + (a + 9b) = -13</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">3a + 19 b = -13 ........ (2)</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Eliminasi a dari persamaan (1) dan (2)</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left.\begin{matrix}a+b=17&space;\\\underline{3a+19b=-13}\end{matrix}\right|\begin{matrix}x3&space;\\x1\end{matrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\left.\begin{matrix}a+b=17 \\\underline{3a+19b=-13}\end{matrix}\right|\begin{matrix}x3 \\x1\end{matrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?\begin{matrix}3a+3b=51\\\underline{3a+19b=-13}-\\-16b=64\\b=\frac{64}{-16}\\b=-4\end{matrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\begin{matrix}3a+3b=51\\\underline{3a+19b=-13}-\\-16b=64\\b=\frac{64}{-16}\\b=-4\end{matrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi beda dari barisan tersebut adalah -4</span></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi b = -4 ke persamaan (1)</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + b = 17</span></p><p style="text-align: justify;"><span style="font-size: medium;">a - 4 = 17</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 17 + 4</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 21</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh :</span></p><p style="text-align: justify;"><span style="font-size: medium;">U6 = a + 5b</span></p><p style="text-align: justify;"><span style="font-size: medium;"> = 21 + 5(-4)</span></p><p style="text-align: justify;"><span style="font-size: medium;"> = 21 - 20</span></p><p style="text-align: justify;"><span style="font-size: medium;"> = 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi besar suku ke-6 adalah 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">17. Diketahui tiga bilangan membentuk barisan aritmatika dengan jumlah ketiga bilangan tersebut 33. Jika hasil kali ketiga bilangan tersenut 1.155. Tentukan ketiga bilangan tersebut.</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><span style="text-align: left;"><span>Misal ketiga bilangan yang membentuk barisan aritmatika adalah </span></span></span><span style="text-align: left;">a, a+b, a+2b</span></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">Dik : a + (a + b) + (a + 2b) = 33</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;"><span> </span><span> </span>a(a+b)(a+2b) = 1.155</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">Dit: U1 = a = ....?</span></p><p><span style="font-size: medium;"><span> </span>U2 = a+b = ....?</span></p><p><span style="font-size: medium;"><span> </span>U3 = a + 2b = ....?</span></p><p><span style="font-size: medium;">Jawab</span></p><p><span style="font-size: medium;">a + (a + b) + (a + 2b) = 33</span></p><p><span style="font-size: medium;">3a + 3b = 33</span></p><p><span style="font-size: medium;">a + b = 11 .....(1)</span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">a(a+b)(a+2b) = 1.155</span></p><p><span style="font-size: medium;">a(a + b)(a+b +b) = 1.155</span></p><p><span style="font-size: medium;">a(11)(11+b) = 1.155</span></p><p><span style="font-size: medium;">a(11 + b) =105</span></p><p><span style="font-size: medium;">dari persamaan (1) diperoleh</span></p><p><span style="font-size: medium;">a = 11 - b</span></p><p><span style="font-size: medium;">maka diperoleh</span></p><p><span style="font-size: medium;">a(11 + b) =105</span></p><p><span style="font-size: medium;">(11 - b)(11 + b) = 105</span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?121-b^{2}=105&space;" title="https://latex.codecogs.com/svg.image?121-b^{2}=105" /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?-b^{2}=105-121" title="https://latex.codecogs.com/svg.image?-b^{2}=105-121" /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?-b^{2}=-16" title="https://latex.codecogs.com/svg.image?-b^{2}=-16" /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b=\pm&space;\sqrt{16}" title="https://latex.codecogs.com/svg.image?b=\pm \sqrt{16}" /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b=\pm&space;4" title="https://latex.codecogs.com/svg.image?b=\pm 4" /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">*) Untuk b = 4</span></p><p><span style="font-size: medium;">Substitusi b = 4 ke persamaan (1)</span></p><p><span style="font-size: medium;">a + b = 11</span></p><p><span style="font-size: medium;">a + 4 = 11</span></p><p><span style="font-size: medium;">a = 11 - 4</span></p><p><span style="font-size: medium;">a = 7</span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">U2 = a + b</span></p><p><span style="font-size: medium;"> = 7 + 4</span></p><p><span style="font-size: medium;"> = 11</span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">U3 = a + 2b</span></p><p><span style="font-size: medium;"> = 7 + 2(4)</span></p><p><span style="font-size: medium;"> = 7 + 8</span></p><p><span style="font-size: medium;"> = 15</span></p><p><span style="font-size: medium;">Jadi ketiga bilangan tersebut adalah 7, 11, 15</span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">**) Untuk b = -4</span></p><p><span style="font-size: medium;">a + b = 11</span></p><p><span style="font-size: medium;">a - 4 = 11</span></p><p><span style="font-size: medium;">a = 11 + 4</span></p><p><span style="font-size: medium;">a = 15</span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">U2 = a + b</span></p><p><span style="font-size: medium;"> = 15 - 4</span></p><p><span style="font-size: medium;"> = 11</span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">U3 = a + 2b</span></p><p><span style="font-size: medium;"> = 15 + 2 (-4)</span></p><p><span style="font-size: medium;"> = 15 - 8= 7</span></p><p><span style="font-size: medium;">Jadi ketiga bilangan tersebut adalah 15, 11, 7</span></p><p><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p><span style="font-size: medium;"><b>Jadi ketiga bilangan tersbut adalah 7, 11, 15 dan 15, 11, 7</b></span></p><p><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">18. Diketahui barisan aritmatika dengan suku ke-n adalah Un. jika U3 = 23 dan U7 = 39, tentukan suku ke-29 barisan tersebut.</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dik: U3 = 23, U7 = 39</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dit : U29 = ....?</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Jawab</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b=\frac{U_{7}-U_{3}}{7-3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b=\frac{U_{7}-U_{3}}{7-3}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span> <img src="https://latex.codecogs.com/svg.image?=\frac{39-23}{7-3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{39-23}{7-3}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span> <img src="https://latex.codecogs.com/svg.image?=\frac{16}{4}=4" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{16}{4}=4" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><blockquote><span style="font-size: medium;">(Cara lain menentukan beda ini dapat dipelajari di link <a href="https://www.sambimatika.my.id/2021/10/barisan-dan-deret-aritmatika-materi-dan.html" rel="nofollow" target="_blank">https://www.sambimatika.my.id/2021/10/barisan-dan-deret-aritmatika-materi-dan.html</a> pada bagian pembahasan contoh 4.)</span></blockquote><p></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi b = 4 ke U3 = 23</span></p><p style="text-align: justify;"><span style="font-size: medium;">U3 = 23</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 2b = 23</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 2(4) = 23</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 8 = 23</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 23 - 8</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 15</span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">U29 = a + 28b</span></p><p style="text-align: justify;"><span style="font-size: medium;"> = 15 + 28(4)</span></p><p style="text-align: justify;"><span style="font-size: medium;"> = 15 + 112</span></p><p><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;"> = 127</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">19. Suku tengah suatu barisan aritmatika adalah 249 dan suku terakhirnya 492. Jika suku ke-7 adalah 73, tentukan suku pertama, beda dan banyak suku barisan tersebut.</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Untuk menjawab soal diatas perhatikan terlebih dahulu ilustrasi berikut.</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE0nk42uEj9sT_EJB4BQEjVSjR-YEs1ABwXWYW8rBW4e5xxDynFtLzwcUYB6m7dztHavEcPKd_OD_bUz6x3AeG6fUEpKxfzSdp_hGJFz_EJURA4zjREzKwOO_WawNObie9sAnQpxNTePvyhYQ0Mm_Gdqq_m20wU637wRerh2kvlQhPetsdnxoDQPVu/s719/suku%20tengah.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Ilustrasi suku tengah dari barisa aritmatika" border="0" data-original-height="486" data-original-width="719" height="432" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE0nk42uEj9sT_EJB4BQEjVSjR-YEs1ABwXWYW8rBW4e5xxDynFtLzwcUYB6m7dztHavEcPKd_OD_bUz6x3AeG6fUEpKxfzSdp_hGJFz_EJURA4zjREzKwOO_WawNObie9sAnQpxNTePvyhYQ0Mm_Gdqq_m20wU637wRerh2kvlQhPetsdnxoDQPVu/w640-h432/suku%20tengah.png" title="Ilustrasi suku tengah dari barisa aritmatika" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;"><a href="https://biggersplinterrattle.com/c6z20r4vgh?key=d5f8540a183d8942b0f24acb83ebdd74" target="_blank">Gambar 1. Ilustrasi Suku Tengah Barisan Aritmatika</a></span></td></tr></tbody></table><p style="text-align: justify;"><span style="font-size: medium;"><span><span style="font-size: medium; text-align: left;"><br /><span><br /></span></span></span></span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Perhatikan pula ilustrasi berikut</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwvyodpAltURb3uAoztRe_f6Z5k8Tkl2xruhkLT2M7iVhTOTP2ZPfklw5rbdxUIzL7yfBoaUV5upJa25hGnw4cyRwR8kzJtwUqqFwl8k-E3XsYEFlzvBSjl-X5eTKOaB4KoN48TXRMj64xi8-CqbIF7l9v-U7Q11WZzNenTqLUFyjGtNhm06DadLE9/s439/beda%20barisan%20aritmatika.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Beda dari suku barisan aritmatika yang tidak berurutan" border="0" data-original-height="248" data-original-width="439" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwvyodpAltURb3uAoztRe_f6Z5k8Tkl2xruhkLT2M7iVhTOTP2ZPfklw5rbdxUIzL7yfBoaUV5upJa25hGnw4cyRwR8kzJtwUqqFwl8k-E3XsYEFlzvBSjl-X5eTKOaB4KoN48TXRMj64xi8-CqbIF7l9v-U7Q11WZzNenTqLUFyjGtNhm06DadLE9/s16000/beda%20barisan%20aritmatika.png" title="Beda dari suku barisan aritmatika yang tidak berurutan" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;"><a href="https://biggersplinterrattle.com/c6z20r4vgh?key=d5f8540a183d8942b0f24acb83ebdd74" target="_blank">Gambar 2. Beda suku barisan aritmatika yang tidak berurutan</a></span></td></tr></tbody></table><p style="text-align: justify;"><span style="font-size: medium;"><span><span style="font-size: medium; text-align: left;"><br /></span></span></span></p><p><span style="font-size: medium;">Berdasarkan ilustrasi diatas barisan aritmatika yang ditanyakan banyak sukunya haruslah ganjil sehingga</span></p><p><span style="font-size: medium;">Diketahui :</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span></span></span></p><div><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Suku tengah = Suku ke 1/2(n + 1) dengan n ganjil</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?U_{tengah}=249" style="text-align: left;" title="https://latex.codecogs.com/svg.image?U_{tengah}=249" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?U_{\frac{1}{2}(n+1)}=249" style="text-align: left;" title="https://latex.codecogs.com/svg.image?U_{\frac{1}{2}(n+1)}=249" /> </span></p><p style="text-align: justify;"><span style="font-size: medium;">Un = 491</span></p><p style="text-align: justify;"><span style="font-size: medium;">U7 = 73</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Misal </span><img src="https://latex.codecogs.com/svg.image?b_{1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{1}" /> adalah beda yang dicari dari suku ke-7 dan suku tengah dan <img src="https://latex.codecogs.com/svg.image?b_{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{2}" /> adalah beda yang dicari dari suku tengah dan suku terakhir, maka diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b_{1}=\frac{U_{\frac{1}{2}(n+1)}-U_{7}}{\frac{1}{2}(n+1)-7}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{1}=\frac{U_{\frac{1}{2}(n+1)}-U_{7}}{\frac{1}{2}(n+1)-7}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{249-73}{\frac{1}{2}n+\frac{1}{2}-7}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{249-73}{\frac{1}{2}n+\frac{1}{2}-7}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{176}{\frac{1}{2}n-\frac{13}{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{176}{\frac{1}{2}n-\frac{13}{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">dan</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b_{2}=\frac{U_{n}-U_{\frac{1}{2}(n+1)}}{n-\frac{1}{2}(n+1)}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{2}=\frac{U_{n}-U_{\frac{1}{2}(n+1)}}{n-\frac{1}{2}(n+1)}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{491-249}{n-\frac{1}{2}n-;\frac{1}{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{491-249}{n-\frac{1}{2}n-\frac{1}{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{242}{\frac{1}{2}n-\frac{1}{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{242}{\frac{1}{2}n-\frac{1}{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Karena barisan aritmatika maka </span><img src="https://latex.codecogs.com/svg.image?b_{1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{1}" /> = <img src="https://latex.codecogs.com/svg.image?b_{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{2}" /> sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b_{1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{1}" /> = <img src="https://latex.codecogs.com/svg.image?b_{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\frac{176}{\frac{1}{2}n-\frac{13}{2}}=\frac{242}{\frac{1}{2}n}-\frac{1}{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\frac{176}{\frac{1}{2}n-\frac{13}{2}}=\frac{242}{\frac{1}{2}n}-\frac{1}{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?176\left&space;(&space;\frac{1}{2}n-\frac{1}{2}&space;\right&space;)=242\left&space;(&space;\frac{1}{2}n-\frac{13}{2}&space;\right&space;)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?176\left ( \frac{1}{2}n-\frac{1}{2} \right )=242\left ( \frac{1}{2}n-\frac{13}{2} \right )" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?88n-88=121n-1.573" style="text-align: left;" title="https://latex.codecogs.com/svg.image?88n-88=121n-1.573" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?121n-88n=1.573-88" style="text-align: left;" title="https://latex.codecogs.com/svg.image?121n-88n=1.573-88" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?33n=1.485" style="text-align: left;" title="https://latex.codecogs.com/svg.image?33n=1.485" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?n=\frac{1.485}{33}=45" style="text-align: left;" title="https://latex.codecogs.com/svg.image?n=\frac{1.485}{33}=45" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh banyak suku dari barisan aritmatika diatas adalah 45, maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?U_{n}=U_{45}=&space;491" style="text-align: left;" title="https://latex.codecogs.com/svg.image?U_{n}=U_{45}= 491" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span><img src="https://latex.codecogs.com/svg.image?U_{tengah}=U_{\frac{1}{2}(45+1)}=U_{23}=249" style="text-align: left;" title="https://latex.codecogs.com/svg.image?U_{tengah}=U_{\frac{1}{2}(45+1)}=U_{23}=249" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi n = 45 ke <img src="https://latex.codecogs.com/svg.image?b_{1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{1}" /> atau <img src="https://latex.codecogs.com/svg.image?b_{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{2}" />., Misal ke <img src="https://latex.codecogs.com/svg.image?b_{1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{1}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b_{1}=\frac{176}{\frac{1}{2}n-\frac{13}{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b_{1}=\frac{176}{\frac{1}{2}n-\frac{13}{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"> <img src="https://latex.codecogs.com/svg.image?=\frac{176}{\frac{45}{2}-\frac{13}{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{176}{\frac{45}{2}-\frac{13}{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span> <img src="https://latex.codecogs.com/svg.image?=\frac{176}{\frac{32}{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{176}{\frac{32}{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span> <img src="https://latex.codecogs.com/svg.image?=\frac{176}{16}=11" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{176}{16}=11" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi beda barisan aritmatika tersebut adalah b = 11</span></p><p style="text-align: justify;"><span style="font-size: medium;">dari U7 = 73 diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;">U7 = 73</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 6b = 73</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 6(11) = 73</span></p><p style="text-align: justify;"><span style="font-size: medium;">a + 66 = 73</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 73 - 66</span></p><p style="text-align: justify;"><span style="font-size: medium;">a = 7</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi diperoleh a = 7, b = 11 dan n = 45</span></p></div><p style="text-align: justify;"><span style="font-size: medium;"><span><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">20. Antara bilangan 440 dan 1.256 disisipkan 15 bilangan sehingga membentuk barisan aritmatika. Tentukan beda dan suku ke-11 barisan tersebut.</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><b>Pembahasan</b></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dik barisan aritmatik 440, 1.256 sehingga diperoleh</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">U1 = a = 440</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">U2 = Un = 1.256</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Dit : b = ....? dan U11 = ....?</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Jika diantara bilangan tersebut disisipkan 15 bilangan sehingga membentuk barisan aritmatika, maka diperoleh barisan aritmatika baru. Perhatikan ilustrasi berikut</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span></span></span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj0vfrK-PqTgK4vWW8PeghaglQZQgsev3Ih0_cr01VJ5zjSje_iIk63LKKmlgRwaWHTn2gr39zoFdpJ4W1GmZzDRmmlJVRPt6cVy83BA7wvHGpFYCul0ENeT9Wnf_MVRWWnd5qF4qVIRAaSuiQAOc_4enUXfCra_Yr7trjr6WaiOjAh1rQ3XyA5-yBn" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Sisipan suku pada barisan aritmatika" data-original-height="187" data-original-width="456" src="https://blogger.googleusercontent.com/img/a/AVvXsEj0vfrK-PqTgK4vWW8PeghaglQZQgsev3Ih0_cr01VJ5zjSje_iIk63LKKmlgRwaWHTn2gr39zoFdpJ4W1GmZzDRmmlJVRPt6cVy83BA7wvHGpFYCul0ENeT9Wnf_MVRWWnd5qF4qVIRAaSuiQAOc_4enUXfCra_Yr7trjr6WaiOjAh1rQ3XyA5-yBn=s16000" title="Sisipan suku pada barisan aritmatika" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">Gambar 3. Sisipan suku pada barisan aritmatika</span></td></tr></tbody></table><p style="text-align: justify;"><span style="font-size: medium;"><span><span style="font-size: medium; text-align: left;"><br />Sehingga dari barisan aritmatika yang baru diperoleh :</span></span></span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">U1 = a = 440 dan U17 = 1.256, maka </span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b=\frac{U_{17}-U_{1}}{17-1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?b=\frac{U_{17}-U_{1}}{17-1}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span> <img src="https://latex.codecogs.com/svg.image?=\frac{1.256-440}{16}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{1.256-440}{16}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span> <img src="https://latex.codecogs.com/svg.image?=\frac{816}{16}=51" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{816}{16}=51" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga</span></p><p style="text-align: justify;"><span style="font-size: medium;">U11 = a + 10b</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span>= 44 + 10(51)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span>= 44 + 510</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span>= 950</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi Barisan aritmatika baru memiliki b = 51 dan U11 = 950</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">21. Diketahui barisan aritmatika 4, 16, 28, 40, ... , 160. Jika diantara dua suku berurutan disisipkan 3 bilangan sehingga terjadi barisan aritmatika baru, tentukan</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">a. Beda barisan baru setelah disisipkan dan</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">b. Suku ke-35 dari barisan baru setelah disisipkan</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Barisan aritmatika awal 4, 16, 28. 40, ... , 160</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">dari barisan awal diketahui a = 4, U2 = 16</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">Bentuk barisan aritmatika baru setelah disisipan tiga bilangan adalah</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><span style="text-align: left;"><span>4, ...., ...., ...., 16, </span></span></span><span style="text-align: left;">...., ...., ...., 28, </span><span style="text-align: left;">...., ...., ...., 40, </span><span style="text-align: left;">... , 160</span></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: left;">dari barisan baru diketahui </span></p><p><span style="font-size: medium;">U1 = a = 4</span></p><p><span style="font-size: medium;">U5 = 16</span></p><p><span style="font-size: medium;">sehingga diperoleh</span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?b=\frac{U_{5}-U_{1}}{5-1}" title="https://latex.codecogs.com/svg.image?b=\frac{U_{5}-U_{1}}{5-1}" /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\frac{16-4}{5-1}" title="https://latex.codecogs.com/svg.image?=\frac{16-4}{5-1}" /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=\frac{12}{4}=3" title="https://latex.codecogs.com/svg.image?=\frac{12}{4}=3" /></span></p><p><span style="font-size: medium;">Maka</span></p><p><span style="font-size: medium;">U35 = a + 34b</span></p><p><span style="font-size: medium;"> = 4 + 34(3)</span></p><p><span style="font-size: medium;"> = 4 + 102</span></p><p><span style="font-size: medium;"> = 106</span></p><p><span style="font-size: medium;">Jadi dari barisan aritmatika baru diperoleh :</span></p><p><span style="font-size: medium;">a. Beda baru, b = 3</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p><span style="font-size: medium;">b. U35 = 106</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Demikian pembahasan </span><span style="text-align: left;"><span> Soal Barisan dan Deret Aritmatika Kelas X Fase E SMA/MA Kurikulum Merdeka, tulisan ini akan terus diupdate untuk memberikan sumber belajar tambahan untuk yang lagi mempelajari barisan deret aritmatika. Semoga bermanfaat.</span></span></span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-19728653108782959152022-10-07T08:34:00.005+08:002022-10-31T17:19:26.175+08:00Pembahasan Soal Matematika SMA/MA Kelas 10 Yang Pernah Ditanyakan di Facebook<p style="text-align: justify;"><span style="font-size: medium;"><b></b></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwoWz0g5b4YNLhU2Tb9yZGUSI-T73W5uEDWnBXg1m0-lIyN7OXssakE0Qprba68a00lvrw9CSYh2B-EjbTPt2ww4jwL3vL_Nwwp8zn97Cf4gbm1jYTlxnguMFnBN9X6dqR8jugMlSFp2baCMGCUSR59-wPEk-dJk5l7V3qIBcRCGQiPLo3LGZ25zU3/s684/facebook%20mat.png" style="margin-left: 1em; margin-right: 1em;"><img alt="Group Matematika Indonesia" border="0" data-original-height="381" data-original-width="684" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwoWz0g5b4YNLhU2Tb9yZGUSI-T73W5uEDWnBXg1m0-lIyN7OXssakE0Qprba68a00lvrw9CSYh2B-EjbTPt2ww4jwL3vL_Nwwp8zn97Cf4gbm1jYTlxnguMFnBN9X6dqR8jugMlSFp2baCMGCUSR59-wPEk-dJk5l7V3qIBcRCGQiPLo3LGZ25zU3/w200-h111/facebook%20mat.png" style="float: left; margin: 5px 9px;" title="Group Matematika Indonesia" width="200" /></a></b></span></div><span style="font-size: medium;"><h2 style="text-align: justify;"><b style="font-weight: bold;"><span style="font-size: medium;">Bagian 1 Pembahasan Soal Matematika SMA/MA Kelas 10 Yang Pernah Ditanyakan di Facebook</span></b></h2><div style="text-align: justify;">Beberapa soal yang ditanyakan oleh siswa di group Matematika Indonesia yang coba saya buatkan pembahasan, semoga bisa bermanfaat.</div></span><p></p><p><span style="font-size: medium;">1. Bentuk lain dari <img src="https://latex.codecogs.com/svg.image?\sqrt{600}" title="https://latex.codecogs.com/svg.image?\sqrt{600}" /> adalah ....</span></p><p><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Bilangan dalam akar harus diubah menjadi perkalian salah satu dari bentuk akar dengan bilangan yang bisa diakarkan langsung.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Bentuk akar adalah akar bilangan yang tidak bisa disederhanakan yaitu 2, 3, 5, 6, 7, 10, 11, 13, 15, 17, 19, 21, 22, 23, 26, 27, 29, 30 dan seterusnya.</span></p><p style="text-align: justify;"><span style="font-size: medium;">2 x 300 = 600 (tidak memenuhi karena <img src="https://latex.codecogs.com/svg.image?\sqrt{300}" title="https://latex.codecogs.com/svg.image?\sqrt{300}" /> masih bisa disederhanakan lagi )</span></p><p style="text-align: justify;"><span style="font-size: medium;">3 x 200 = 600 (tidak memenuhi karena <img src="https://latex.codecogs.com/svg.image?\sqrt{200}" title="https://latex.codecogs.com/svg.image?\sqrt{200}" /> masih bisa disederhanakan lagi )</span></p><p style="text-align: justify;"><span style="font-size: medium;">5 x 120 = 600 (tidak memenuhi karena <img src="https://latex.codecogs.com/svg.image?\sqrt{120}" title="https://latex.codecogs.com/svg.image?\sqrt{120}" /> masih bisa disederhanakan lagi</span></p><p style="text-align: justify;"><span style="font-size: medium;">6 x 100 = 600 (Memenuhi)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka</span></p>
<p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\sqrt{600}=\sqrt{100.6}=\sqrt{100}.\sqrt{6}=10\sqrt{6}" title="https://latex.codecogs.com/svg.image?\sqrt{600}=\sqrt{100.6}=\sqrt{100}.\sqrt{6}=10\sqrt{6}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Jadi bentuk lain dari <img src="https://latex.codecogs.com/svg.image?\sqrt{600}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\sqrt{600}" /> adalah <img src="https://latex.codecogs.com/svg.image?10\sqrt{6}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?10\sqrt{6}" /> </span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\blacksquare" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Untuk pembahasa bentuk akar juga dapat dipelajari melalui link <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/pembahasan-soal-bentuk-akar-matematika.html" rel="" target="_blank">https://matematikasmpmts.sambimatika.my.id/2021/08/pembahasan-soal-bentuk-akar-matematika.html</a></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>2. Perhatikan persamaan berikut </span><img src="https://latex.codecogs.com/svg.image?\left\{\begin{matrix}&space;-x+5y=7\\2x-y=-5\end{matrix}\right." style="text-align: left;" title="https://latex.codecogs.com/svg.image?\left\{\begin{matrix} -x+5y=7\\2x-y=-5\end{matrix}\right." /> Hasil dari 7<i>x</i> + 3<i>y</i> = .....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pada pembahasan ini digunakan Metode Subtitusi, untuk metode eliminasi dan gabungan eliminasi subtitusi silahkan dikerjakan sendiri.</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>- x</i> + 5<i>y</i> = 7 ........ (1)</span></p><p style="text-align: justify;"><span style="font-size: medium;">2<i>x - y</i> = <i>-</i>5 ........... (2)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ubah persamaan (1) menjadi bentuk <i>x</i> =</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>- x</i> + 5<i>y</i> = 7 (<i>Kurangi kedua ruas dengan 5y</i>)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>- x</i> + 5<i>y - </i>5<i>y</i> = 7 - 5<i>y</i></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>- x</i> = 7 <i>-</i> 5<i>y</i> (<i>Kalikan kedua ruas dengan - 1</i>)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>x</i> = <i>-</i>7 + 5<i>y</i> (<i>Lakukan perubahan tempat. Langkah ini bisa tidak dilakukan</i>)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>x</i> = 5<i>y -</i> 7 ......(3)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi persamaan (3) ke persamaan (2)</span></p><p style="text-align: justify;"><span style="font-size: medium;">2<i>x - y</i> = <i>-</i>5</span></p><p style="text-align: justify;"><span style="font-size: medium;">2(5<i>y -</i> 7) <i>- y</i> = <i>-</i>5</span></p><p style="text-align: justify;"><span style="font-size: medium;">10<i>y -</i> 14 <i>- y</i> = <i>-</i>5 (<i>urutkan</i>)</span></p><p style="text-align: justify;"><span style="font-size: medium;">10<i>y - y - </i>14 = <i>-</i>5</span></p><p style="text-align: justify;"><span style="font-size: medium;">9<i>y -</i> 14 = <i>-</i>5 (<i>Tambah kedua ruas dengan 14</i>)</span></p><p style="text-align: justify;"><span style="font-size: medium;">9<i>y - </i>14 + 14 = <i>-</i>5 + 14</span></p><p style="text-align: justify;"><span style="font-size: medium;">9<i>y</i> = 9 (<i>Bagi kedua ruas dengan</i> 9)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>y</i> = 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi <i>y</i> = 1 ke persamaan (3)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>x</i> = 5<i>y - </i>10</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>x</i> = 5.1 <i>- </i>10</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>x</i> = 5<i> - </i>10</span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>x</i> = <i>-</i>5</span></p><p style="text-align: justify;"><span style="font-size: medium;">Subtitusi <i>x = -</i>5 dan <i>y =</i> 1 ke persamaan yang ditanyakan</span></p><p style="text-align: justify;"><span style="font-size: medium;">7<i>x</i> + 3<i>y</i> = 7(<i>-</i>5) + 3(1) = <i>-</i>35 + 3 = <i>-</i>32</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span><span>Jadi </span><span>7</span><i>x</i><span> + 3</span><i>y</i><span> = </span><i>-</i><span>32 </span></span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\blacksquare" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Untuk pembahasan lebih lanjut tentang Sistem persamaan linier tiga variabel dapat dipelajari melalu link <a href="https://www.sambimatika.my.id/2021/10/solusi-spltv-dengan-metode-substitusi.html" rel="" target="_blank">https://www.sambimatika.my.id/2021/10/solusi-spltv-dengan-metode-substitusi.html</a></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>3. Hasil dari </span><img src="https://latex.codecogs.com/svg.image?\frac{5^{6}x9^{4}}{15^{5}}=...." style="text-align: left;" title="https://latex.codecogs.com/svg.image?\frac{5^{6}x9^{4}}{15^{5}}=...." /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\frac{5^{6}x9^{4}}{15^{5}}=\frac{5^{6}x(3^{2})^{4}}{(3x5)^{5}}" title="https://latex.codecogs.com/svg.image?\frac{5^{6}x9^{4}}{15^{5}}=\frac{5^{6}x(3^{2})^{4}}{(3x5)^{5}}" /></span></p>
<p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{5^{6}x3^{8}}{3^{5}x5^{5}}" title="https://latex.codecogs.com/svg.image?=\frac{5^{6}x3^{8}}{3^{5}x5^{5}}" /> </span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=5^{6-5}x3^{8-5}" title="https://latex.codecogs.com/svg.image?=5^{6-5}x3^{8-5}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=5x3^{3}" title="https://latex.codecogs.com/svg.image?=5x3^{3}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=5x27=135" title="https://latex.codecogs.com/svg.image?=5x27=135" /> </span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" title="https://latex.codecogs.com/svg.image?\blacksquare" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Untuk mempelajari lebih jauh dasar-dasar perpangkatan dapat dipelajari melalui link <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/pembahasan-soal-perpangkatan-matematika.html" rel="" target="_blank">https://matematikasmpmts.sambimatika.my.id/2021/08/pembahasan-soal-perpangkatan-matematika.html</a></span></p><p style="text-align: left;"><span style="font-size: medium;"><span><br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span>4. Bentuk sederhana dari </span><img src="https://latex.codecogs.com/svg.image?4^{5}.4^{2}" title="https://latex.codecogs.com/svg.image?4^{5}.4^{2}" /> adalah ....</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?4^{5}.4^{2}=4^{5+2}" title="https://latex.codecogs.com/svg.image?4^{5}.4^{2}=4^{5+2}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=4^{7}" title="https://latex.codecogs.com/svg.image?=4^{7}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=(2^{2})^{7}" title="https://latex.codecogs.com/svg.image?=(2^{2})^{7}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=2^{2.7}" title="https://latex.codecogs.com/svg.image?=2^{2.7}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=2^{14}" title="https://latex.codecogs.com/svg.image?=2^{14}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span><span> </span><span> </span>= 16.834 </span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" title="https://latex.codecogs.com/svg.image?\blacksquare" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span>5. Bentuk lain dari </span><img src="https://latex.codecogs.com/svg.image?\frac{(6C^{3})^{2}}{2C^{4}}" title="https://latex.codecogs.com/svg.image?\frac{(6C^{3})^{2}}{2C^{4}}" /> adalah ....</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\frac{(6C^{3})^{2}}{2C^{4}}=\frac{6^{2}C^{3.2}}{2C^{4}}" title="https://latex.codecogs.com/svg.image?\frac{(6C^{3})^{2}}{2C^{4}}=\frac{6^{2}C^{3.2}}{2C^{4}}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{36C^{6}}{2C^{4}}" title="https://latex.codecogs.com/svg.image?=\frac{36C^{6}}{2C^{4}}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=18C^{6-4}" title="https://latex.codecogs.com/svg.image?=18C^{6-4}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=18C^{2}" title="https://latex.codecogs.com/svg.image?=18C^{2}" /> <img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" title="https://latex.codecogs.com/svg.image?\blacksquare" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">6. Tiga bersaudara Ina, Ani dan Nia berbelanja di toko "ROTI BAKAR". Mereka membeli roti dengan berbagai macam rasa yang terdiri dari cokelat, stroberi dan keju. Ina membeli roti dengan rasa 1 cokelat, 2 stroberi dan 3 keju seharga Rp. 23.000,00. Ani membeli roti dengan rasa 4 cokelat, 2 stroberi dan 1 keju seharga Rp. 22.000,00. Nia membeli roti dengan 1 rasa cokelat, 7 stroberi dan 1 keju seharga Rp. 25.500,00.. Persamaan linier yang sesuai pada cerita diatas adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">7. Ibu memberikan uang sebesar Rp. 50.000,00- kepada Ina. Jika ibu menyuruh Ina untuk membeli roti bakar dengan rasa 3 cokelat, 4 stroberi dan 2 keju, maka uang kembalian yang akan diberikan Ina kepada Ibu adalah .....</span></p><p style="text-align: justify;"><span style="font-size: medium;">8. Dari cerita tiga bersaudara yang berbelanja di toko "ROTI BAKAR" diperoleh harga satuan untuk Roti Bakar rasa cokelat adalah....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>9. </span>Dari cerita tiga bersaudara yang berbelanja di toko "ROTI BAKAR" diperoleh harga satuan untuk Roti Bakar rasa stroberi adalah....</span></p><p style="text-align: justify;"><span style="font-size: medium;">10. Dari cerita tiga bersaudara yang berbelanja di toko "ROTI BAKAR" diperoleh harga satuan untuk Roti Bakar rasa keju adalah....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawaban soal no 6</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal x = cokelat, y = stroberi dan z = keju</span></p><p style="text-align: justify;"><span style="font-size: medium;">Pembelian roti Ina, Ani dan Nia seperti pada tabel berikut</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhm18VTlxNImetRH0wR1B-r3oLPvyJRYHzkZFb1rypsG5bWrnAs0YcvWoYRemVN0l3mIqo5iVA-vaLp8FLqmUxN9KFjCEOA5H_lXLiczYixMHG611BqnGJwZYPP2sdb9-Ly4mNhNpZ0ClfQctqoj15nKkzLhKgOE8sSUTa9r6NFDq6UJJfSOCQZ8tyG" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Tabel Pembelian roti" data-original-height="143" data-original-width="755" height="122" src="https://blogger.googleusercontent.com/img/a/AVvXsEhm18VTlxNImetRH0wR1B-r3oLPvyJRYHzkZFb1rypsG5bWrnAs0YcvWoYRemVN0l3mIqo5iVA-vaLp8FLqmUxN9KFjCEOA5H_lXLiczYixMHG611BqnGJwZYPP2sdb9-Ly4mNhNpZ0ClfQctqoj15nKkzLhKgOE8sSUTa9r6NFDq6UJJfSOCQZ8tyG=w640-h122" title="Tabel Pembelian roti" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">Tabel Pembelian roti di toko " ROTI BAKAR"</span></td></tr></tbody></table><span style="font-size: medium;"><br />Dari tabel diatas persamaan liniernya adalah</span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Ina : x + 2y + 3z = 23.000</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ani : 4x + 2y + z = 22.000</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Nia : x + 7y + z = 25.500 </span><img src="https://latex.codecogs.com/svg.image?\blacksquare&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\blacksquare" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Jawaban soal no.7</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sistem persamaan linier dari kasus diatas adalah </span></p>
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left\{\begin{matrix}x+2y+3z=23000&space;\\4x+2y+z=22000&space;\\x+7y+z=25500\end{matrix}\right." title="https://latex.codecogs.com/svg.image?\left\{\begin{matrix}x+2y+3z=23000 \\4x+2y+z=22000 \\x+7y+z=25500\end{matrix}\right." /></span><p style="text-align: left;"><span style="font-size: medium;">Misal</span></p><p style="text-align: justify;"><span style="font-size: medium;">x + 2y + 3z = 23000 .......(1)</span></p><p style="text-align: justify;"><span style="font-size: medium;">4x + 2y + z = 22000 .......(2)</span></p><p style="text-align: justify;"><span style="font-size: medium;">x + 7y + z = 25500 .........(3)</span></p><p style="text-align: justify;"><span style="font-size: medium;">Eliminasi z dari persamaan (1) dan (2)</span></p>
<p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left.\begin{matrix}x+2y+3z=23000\\&space;\underline{4x+2y+z=22000&space;}\end{matrix}\right|\begin{matrix}x1&space;\\x3\end{matrix}" title="https://latex.codecogs.com/svg.image?\left.\begin{matrix}x+2y+3z=23000\\ \underline{4x+2y+z=22000 }\end{matrix}\right|\begin{matrix}x1 \\x3\end{matrix}" /></span></p>
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}&space;x+2y+3z=23000\\\underline{12x+6y+3z=66000&space;-}\\-11x-4y=-43000\\11x+4y=43000\end{matrix}" title="https://latex.codecogs.com/svg.image?\begin{matrix} x+2y+3z=23000\\\underline{12x+6y+3z=66000 -}\\-11x-4y=-43000\\11x+4y=43000\end{matrix}" /></span><p style="text-align: left;"><span style="font-size: medium;">Misal 11x + 4y = 43000 .........(4)</span></p><p style="text-align: left;"><span style="font-size: medium;">Eliminasi z dari persamaan (1) dan (3)</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left.\begin{matrix}x+2y+3z=23000\\x+7y+z=25500\end{matrix}\right|\begin{matrix}x1&space;\\x3\end{matrix}" title="https://latex.codecogs.com/svg.image?\left.\begin{matrix}x+2y+3z=23000\\x+7y+z=25500\end{matrix}\right|\begin{matrix}x1 \\x3\end{matrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}x+2y+3z=23000&space;\\\underline{3x+21y+3z=76500-}\\-2x-19y=-53500\\2x+19y=53500\end{matrix}" title="https://latex.codecogs.com/svg.image?\begin{matrix}x+2y+3z=23000 \\\underline{3x+21y+3z=76500-}\\-2x-19y=-53500\\2x+19y=53500\end{matrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Misal 2x + 19y = 53500 .......(5)</span></p><p style="text-align: left;"><span style="font-size: medium;">Eliminasi x dari persamaan (4) dan (5)</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left.\begin{matrix}11x+4y=43000&space;\\2x+19y=53500\end{matrix}\right|\begin{matrix}x2&space;\\x11\end{matrix}" title="https://latex.codecogs.com/svg.image?\left.\begin{matrix}11x+4y=43000 \\2x+19y=53500\end{matrix}\right|\begin{matrix}x2 \\x11\end{matrix}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\begin{matrix}22x+8y=86000&space;\\\underline{22x+209y=588500-}\\-201y=-502500\\y=2500\end{matrix}" title="https://latex.codecogs.com/svg.image?\begin{matrix}22x+8y=86000 \\\underline{22x+209y=588500-}\\-201y=-502500\\y=2500\end{matrix}" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Substitusi y = 2500 ke persamaan (4)</span></p><p style="text-align: left;"><span style="font-size: medium;">11x + 4y = 43000</span></p><p style="text-align: left;"><span style="font-size: medium;">11x + 4(2500) = 43000</span></p><p style="text-align: left;"><span style="font-size: medium;">11x + 10000 = 43000</span></p><p style="text-align: left;"><span style="font-size: medium;">11x = 33000</span></p><p style="text-align: left;"><span style="font-size: medium;">x = 3000</span></p><p style="text-align: left;"><span style="font-size: medium;">Substitusi x = 3000 dan y = 2500 ke persamaan (1)</span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">x + 2y + 3z = 23000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">3000 + 2(2500) + 3z = 23000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">3000 + 5000 + 3z = 23000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">8000 + 3z = 23000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">3z = 15000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">z = 5000</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="text-align: justify;">Harga beli </span><span style="text-align: justify;">roti bakar dengan rasa 3 cokelat, 4 stroberi dan 2 keju adalah</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">HB = 3x + 4y + 2z</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 3(3000) + 4(2500) +2(5000)</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 9000 + 10000 + 10000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;"><span> </span>= 29000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">Maka uang kembalian yang akan diberikan Ani ke ibu = 50000-29000 = 21000</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;">Jadi uang yang dikembalikan Ani ke Ibu adalah Rp. 21.000,00-</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: left;"><span style="text-align: justify;"><b><span style="font-size: medium;">Jawaban soal no 8</span></b></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="text-align: justify;">Karena x = Roti bakar rasa cokelat, maka </span><span style="text-align: justify;">harga satuan untuk Roti Bakar rasa cokelat adalah Rp. 3.000,00-</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><b><span style="font-size: medium;">Jawaban soal no 9</span></b></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="text-align: justify;">Karena y = Roti bakar rasa stroberi, maka </span><span style="text-align: justify;">harga satuan untuk Roti Bakar rasa stroberi adalah Rp. 2.500,00-</span></span></p><p style="text-align: left;"><span style="text-align: justify;"><b><span style="font-size: medium;">Jawaban soal no 10</span></b></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="text-align: justify;">Karena z = Roti bakar rasa keju, maka </span><span style="text-align: justify;">harga satuan untuk Roti Bakar rasa keju adalah Rp. 5.000,00-</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="text-align: justify;"><br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span><span style="text-align: justify;">11. </span></span><img src="https://latex.codecogs.com/svg.image?2\sqrt{3}\left&space;(&space;\sqrt{8}+3\sqrt{3}&space;\right&space;)=...." title="https://latex.codecogs.com/svg.image?2\sqrt{3}\left ( \sqrt{8}+3\sqrt{3} \right )=...." /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?2\sqrt{3}\left&space;(&space;\sqrt{8}+3\sqrt{3}&space;\right&space;)=2\sqrt{3}\left&space;(&space;2\sqrt{2}+3\sqrt{3}&space;\right&space;)" title="https://latex.codecogs.com/svg.image?2\sqrt{3}\left ( \sqrt{8}+3\sqrt{3} \right )=2\sqrt{3}\left ( 2\sqrt{2}+3\sqrt{3} \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=2\sqrt{3}\left&space;(&space;2\sqrt{2}&space;\right&space;)+2\sqrt{3}\left&space;(&space;3\sqrt{3}&space;\right&space;)" title="https://latex.codecogs.com/svg.image?=2\sqrt{3}\left ( 2\sqrt{2} \right )+2\sqrt{3}\left ( 3\sqrt{3} \right )" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=2.2.\sqrt{3}.\sqrt{2}+2.3.\sqrt{3}.\sqrt{3}" title="https://latex.codecogs.com/svg.image?=2.2.\sqrt{3}.\sqrt{2}+2.3.\sqrt{3}.\sqrt{3}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=4\sqrt{2.3}+6\sqrt{3.3}" title="https://latex.codecogs.com/svg.image?=4\sqrt{2.3}+6\sqrt{3.3}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=4\sqrt{6}+6\sqrt{9}" title="https://latex.codecogs.com/svg.image?=4\sqrt{6}+6\sqrt{9}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=4\sqrt{6}+6.3" title="https://latex.codecogs.com/svg.image?=4\sqrt{6}+6.3" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?=4\sqrt{6}+18" title="https://latex.codecogs.com/svg.image?=4\sqrt{6}+18" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span>12. Jika </span><img src="https://latex.codecogs.com/svg.image?x=\frac{1}{8}" title="https://latex.codecogs.com/svg.image?x=\frac{1}{8}" /> dan y = 81 maka nilai dari
<img src="https://latex.codecogs.com/svg.image?\frac{2}{3}x^{-\frac{1}{3}}.y^{\frac{1}{4}}" title="https://latex.codecogs.com/svg.image?\frac{2}{3}x^{-\frac{1}{3}}.y^{\frac{1}{4}}" /> adalah ......</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\frac{2}{3}x^{-\frac{1}{3}}.y^{\frac{1}{4}}=\frac{2}{3}\left&space;(&space;\frac{1}{8}&space;\right&space;)^{-\frac{1}{3}}.\left&space;(&space;81&space;\right&space;)^{\frac{1}{4}}" title="https://latex.codecogs.com/svg.image?\frac{2}{3}x^{-\frac{1}{3}}.y^{\frac{1}{4}}=\frac{2}{3}\left ( \frac{1}{8} \right )^{-\frac{1}{3}}.\left ( 81 \right )^{\frac{1}{4}}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{2}{3}\left&space;(&space;\frac{1}{2^{3}}&space;\right&space;)^{-\frac{1}{3}}.\left&space;(&space;3^{4}&space;\right&space;)^{\frac{1}{4}}" title="https://latex.codecogs.com/svg.image?=\frac{2}{3}\left ( \frac{1}{2^{3}} \right )^{-\frac{1}{3}}.\left ( 3^{4} \right )^{\frac{1}{4}}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{2}{3}\left&space;(&space;2^{-3}&space;\right&space;)^{-\frac{1}{3}}.\left&space;(&space;3^{4}&space;\right&space;)^{\frac{1}{4}}" title="https://latex.codecogs.com/svg.image?=\frac{2}{3}\left ( 2^{-3} \right )^{-\frac{1}{3}}.\left ( 3^{4} \right )^{\frac{1}{4}}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{2}{3}.2.3=2.2=4" title="https://latex.codecogs.com/svg.image?=\frac{2}{3}.2.3=2.2=4" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span>13. Bentuk lain dari </span><img src="https://latex.codecogs.com/svg.image?\left&space;(3^{2}a^{5}&space;&space;\right&space;)^{2}" title="https://latex.codecogs.com/svg.image?\left (3^{2}a^{5} \right )^{2}" /> adalah ....</span></p><p style="text-align: left;">
<span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\left&space;(3^{2}a^{5}&space;&space;\right&space;)^{2}=\left&space;(&space;3^{2}&space;\right&space;)^{2}\left&space;(&space;a^{5}&space;\right&space;)^{2}" title="https://latex.codecogs.com/svg.image?\left (3^{2}a^{5} \right )^{2}=\left ( 3^{2} \right )^{2}\left ( a^{5} \right )^{2}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=3^{2.2}.a^{5.2}" title="https://latex.codecogs.com/svg.image?=3^{2.2}.a^{5.2}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=3^{4}.a^{10}" title="https://latex.codecogs.com/svg.image?=3^{4}.a^{10}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=81a^{10}" title="https://latex.codecogs.com/svg.image?=81a^{10}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">14. Hasil dari <img src="https://latex.codecogs.com/svg.image?\sqrt[4]{25^{6}}" title="https://latex.codecogs.com/svg.image?\sqrt[4]{25^{6}}" /> adalah ....</span></p><p style="text-align: left;"><span style="font-size: medium;">
Pembahasan</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\sqrt[4]{25^{6}}=\left&space;(&space;25^{6}&space;\right&space;)^{\frac{1}{4}}=\left&space;(&space;\left&space;(&space;5^{2}&space;\right&space;)^{6}&space;\right&space;)^{\frac{1}{4}}=5^{2.6.\frac{1}{4}}=5^{3}=125" title="https://latex.codecogs.com/svg.image?\sqrt[4]{25^{6}}=\left ( 25^{6} \right )^{\frac{1}{4}}=\left ( \left ( 5^{2} \right )^{6} \right )^{\frac{1}{4}}=5^{2.6.\frac{1}{4}}=5^{3}=125" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-size: medium;">15. <img src="https://latex.codecogs.com/svg.image?\frac{1}{8}" title="https://latex.codecogs.com/svg.image?\frac{1}{8}" /> senilai dengan ......</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>
Pembahasan</b></span></p><p style="text-align: left;"><span style="font-size: medium;">Jika dibuat dalam bentuk bilangan desimal maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\frac{1}{8}=0,125" title="https://latex.codecogs.com/svg.image?\frac{1}{8}=0,125" /> </span></p><p style="text-align: left;"><span style="font-size: medium;">Jika dibuat dalam bentuk persen maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\frac{1}{8}=12,5%" title="https://latex.codecogs.com/svg.image?\frac{1}{8}=12,5%" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Jika mau dibuat dalam bentuk perpangkatan maka</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\frac{1}{8}=2^{-3}" title="https://latex.codecogs.com/svg.image?\frac{1}{8}=2^{-3}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Demikian pembahasan beberapa soal matematika SMA/MA kelas 10 yang pernah ditanyakan di facebook dan selanjutnya kami akan bahas soal-soal lainnya pada bagian selanjutnya. Semoga bermanfaat</span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-69808061408412268952022-10-03T21:36:00.006+08:002022-10-31T17:23:45.478+08:00Langkah-Langkah Membuat Microsite di Shortlink s.id<p style="text-align: justify;"><span style="font-size: medium;"><b>Langkah-Langkah Membuat Microsite di Shortlink s.id -</b> Bagi seorang Instruktur, Fasilitator ataupun guru yang sedang melaksanakan suatu pelatihan atau pembelajaran, tetapi belum memiliki website atau webblog dapat tampil profesional dengan memanfaatkan fitur Microsite dari platform shortlink s.id secara gratis yang dapat dijadikan sebagai elearning sederhana dengan tampilan yang elegan dan profesional.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Berikut langkah-langkah membuat microsite di shortlink s.id</span></p><h2 style="text-align: justify;"><span style="font-size: medium;"><b>MEMBUAT AKUN DI s.id</b></span></h2><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Siapkan email anda, misal "namaemail"@gmail.com</span></li><li><span style="font-size: medium;">Bagi yang belum memiliki akun di s.id, lakukan pendaftaran terlebih dahulu.</span></li><li><span style="font-size: medium;">Pada kotak Address Bar, ketik s.id atau klik link ini <a href="http://s.id" rel="nofollow" target="_blank">s.id</a></span></li><li><span style="font-size: medium;">Dari halaman home.s.id, klik tombol <b>Login/Register</b></span></li></ul><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN8M6NTmmZ3MZgXe9GV9YqdTbW-AoikGDWucjGHGyGqbqIrxr7cJARnH3Xqn-kGSJfQn_LASew7H4SIzT1s-oQ22myC_1aM7qJoINZW1kJIzc3GPa7AdoCkRpyChkrobiUZpTPVmsnFQc-4exFLHDFfpOfonbKWWsLUrPAXGKdeN4AIx6WJPVFR7gF/s1366/sid%201.png" style="margin-left: auto; margin-right: auto;"><img alt="Home s.id" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN8M6NTmmZ3MZgXe9GV9YqdTbW-AoikGDWucjGHGyGqbqIrxr7cJARnH3Xqn-kGSJfQn_LASew7H4SIzT1s-oQ22myC_1aM7qJoINZW1kJIzc3GPa7AdoCkRpyChkrobiUZpTPVmsnFQc-4exFLHDFfpOfonbKWWsLUrPAXGKdeN4AIx6WJPVFR7gF/w640-h360/sid%201.png" title="Home s.id" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1 Halaman Home s.id</td></tr></tbody></table><br /><p style="text-align: left;"></p><ul style="text-align: left;"><li><span style="font-size: medium;">Klik <b>Sign in with Google</b></span></li></ul><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggfxtI2R_x0gcssH0Tdo8wlQ2j-kRV44ONMhLfVu0sidsNuqfNfYCFXo7rXIdbwBllh1iO81CLH66FLS89h4MVSC5Ts-Yhqj_GPeBRYV3WCJxlyl0120PnH6dKzIktD9kGY3MUgEdaDzqd4qihqWEAcS7J9GEqAJSaX4ErYxORllEOFA2yqWmJ4I4L/s1366/sid%202.png" style="margin-left: auto; margin-right: auto;"><img alt="Login dengan akun google" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggfxtI2R_x0gcssH0Tdo8wlQ2j-kRV44ONMhLfVu0sidsNuqfNfYCFXo7rXIdbwBllh1iO81CLH66FLS89h4MVSC5Ts-Yhqj_GPeBRYV3WCJxlyl0120PnH6dKzIktD9kGY3MUgEdaDzqd4qihqWEAcS7J9GEqAJSaX4ErYxORllEOFA2yqWmJ4I4L/w640-h360/sid%202.png" title="Login dengan akun google" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Login dengan akun google</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Masukkan akun google anda.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Klik tombol <b>Berikutnya</b>, lalu masukkan sandi akun anda dan selesaikan proses login</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZK1iZOIzceegx9R6gL-2QvDXiHLdVw0plmkenr5O63CxO4a3PH9TF9repyMgMJEt0WXnKVlbxOcBLSj1DpkZabhGSHV_k8TDTAT-xYPjVgK000ZkzArWckaM11jKj_4Jl09T5Kk9kWMrA2jxm_TJdFm3OY05biztnhcpsp-dDN8c0kg3JBdfUrrhz/s1366/sid%203.png" style="margin-left: auto; margin-right: auto;"><img alt="Masukkan akun Google" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZK1iZOIzceegx9R6gL-2QvDXiHLdVw0plmkenr5O63CxO4a3PH9TF9repyMgMJEt0WXnKVlbxOcBLSj1DpkZabhGSHV_k8TDTAT-xYPjVgK000ZkzArWckaM11jKj_4Jl09T5Kk9kWMrA2jxm_TJdFm3OY05biztnhcpsp-dDN8c0kg3JBdfUrrhz/w640-h360/sid%203.png" title="Masukkan akun Google" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Masukkan akun Google</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Setelah berhasil akan muncul halaman ini. Centang kedua kotak lalu klik tombol <b>Continue</b></span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLXHo3Ofux5RmjyEDuFh8wD3SkbDAH5SC2Ihf4k2Vjylms0y92SWjucGXIo_649FW12Jssav7s9BcAZSyBbWDfsvm29r7KfaTIUZdYMT_5kDvK5j5-y2qwZVjw-IGxj1RJhrgviB3t3gUZh0Ufh3_f0M40Of4zd8moQRc4z4jL3WxfHHs9ORqbl6yO/s1366/sid%204.png" style="margin-left: auto; margin-right: auto;"><img alt="Halaman Aouth s.id" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLXHo3Ofux5RmjyEDuFh8wD3SkbDAH5SC2Ihf4k2Vjylms0y92SWjucGXIo_649FW12Jssav7s9BcAZSyBbWDfsvm29r7KfaTIUZdYMT_5kDvK5j5-y2qwZVjw-IGxj1RJhrgviB3t3gUZh0Ufh3_f0M40Of4zd8moQRc4z4jL3WxfHHs9ORqbl6yO/w640-h360/sid%204.png" title="Halaman Aouth s.id" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Halaman Auth login</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Tunggu proses, jika berhasil akan tampil halaman dashboard akun s.id kita, seperti gambar berikut</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1E7UDWvXwe_PDGgjHukHCiOolzO1HUBSDcdrGMvhYXFVvH6RPCvtPK2qwsV60cSQfG269qnaUTeGtResC8fAqwzkW01_bwWBvDlfkC43cgnKTrXnvgCQ2wdFiHmzAylSRU09v8lXChSXxQBItb_cuSIfy2-xIlT6OV7E30r3GTqhBWxDV_QlGyrPM/s1366/sid%205.png" style="margin-left: auto; margin-right: auto;"><img alt="Halaman Dashboard akun s.id" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1E7UDWvXwe_PDGgjHukHCiOolzO1HUBSDcdrGMvhYXFVvH6RPCvtPK2qwsV60cSQfG269qnaUTeGtResC8fAqwzkW01_bwWBvDlfkC43cgnKTrXnvgCQ2wdFiHmzAylSRU09v8lXChSXxQBItb_cuSIfy2-xIlT6OV7E30r3GTqhBWxDV_QlGyrPM/w640-h360/sid%205.png" title="Halaman Dashboard akun s.id" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Halaman Dashboard akun s.id anda</td></tr></tbody></table><br /><h2 style="text-align: left;"><b><span style="font-size: medium;">MEMBUAT SHORT LINK (Memperpendek Link)</span></b></h2><p style="text-align: left;"></p><ul style="text-align: left;"><li><span style="font-size: medium;">Misal, ambil link berbagi file di Google Drive</span></li><li><span style="font-size: medium;">Klik <b>Menu Links</b> di bawah Dashboard</span></li></ul><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj57DN-TexK918DI1CTScMRR6SpzgPfpFPpavkdgWKw2XF0RQZirFqOd2pKGkWiGlw2FfT6lb6Ki3kzT7EsucblzbYj0k2XB_65PMksMBwiVyYmciPYNmdgUlAWQxNpmGStyc9FknFDtBWoJ1XiHLckebyoN0FUlPwDqn4G_caPa2Ve0ih8CQPA5ZlI/s1366/sid%206.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Short Link" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj57DN-TexK918DI1CTScMRR6SpzgPfpFPpavkdgWKw2XF0RQZirFqOd2pKGkWiGlw2FfT6lb6Ki3kzT7EsucblzbYj0k2XB_65PMksMBwiVyYmciPYNmdgUlAWQxNpmGStyc9FknFDtBWoJ1XiHLckebyoN0FUlPwDqn4G_caPa2Ve0ih8CQPA5ZlI/w640-h360/sid%206.png" title="Membuat Short Link" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Langkah 1 Membuat Short Link</td></tr></tbody></table><br /><p style="text-align: left;"></p><ul style="text-align: left;"><li><span style="font-size: medium;">Paste link yang diperoleh dari langkah 1 ke kotak Short it (Tekan <b>Control + V</b>)</span></li><li><span style="font-size: medium;">Lalu Klik Tombol <b>Short it!</b></span></li></ul><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinvetfuJzAvLmaWmgxjXabDyHyP7Ch7qGYH4n3IJff4uo8wxT16SF-I1TDEsKn2oMqI7qUlfhOil4q2BfSglPA2raX85Gxyi7l4PO7kO20L1g6AHcjTPuXj3UKM0J0XBX_sEqAuTIikrwgyvVCEqLSZtqlavr53KOUCitzrF8GdlJQGULKDuX9PurD/s1366/sid%207.png" style="margin-left: auto; margin-right: auto;"><img alt="Memasukkan link ke kotak Short it" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinvetfuJzAvLmaWmgxjXabDyHyP7Ch7qGYH4n3IJff4uo8wxT16SF-I1TDEsKn2oMqI7qUlfhOil4q2BfSglPA2raX85Gxyi7l4PO7kO20L1g6AHcjTPuXj3UKM0J0XBX_sEqAuTIikrwgyvVCEqLSZtqlavr53KOUCitzrF8GdlJQGULKDuX9PurD/w640-h360/sid%207.png" title="Memasukkan link ke kotak Short it" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Langkah 2 shot link di s.id</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Sistem akan memperpendek link kita secara otomatis, seperti gambar berikut, lalu tutup kotak tersebut</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglNTKTwJUXe4qOk2-siLRO3TX2ZpLcj_k8ToKGWe0sfIWSZ6gYN_-VlcwOfBRYVPpzAZU0PNMkO1pZNt1p4tQf3q_x98FAMyR7FlYQcnb8qb3D0Qi-S9DiGEcHglIkHjLkuYGk1wPlH1WUYNYbImBF3srI8Pyhfkg6-x7jpyRYsLE5X_FunoR_vV15/s1366/sid%208.png" style="margin-left: auto; margin-right: auto;"><img alt="Short Link Berhasil dibuat" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglNTKTwJUXe4qOk2-siLRO3TX2ZpLcj_k8ToKGWe0sfIWSZ6gYN_-VlcwOfBRYVPpzAZU0PNMkO1pZNt1p4tQf3q_x98FAMyR7FlYQcnb8qb3D0Qi-S9DiGEcHglIkHjLkuYGk1wPlH1WUYNYbImBF3srI8Pyhfkg6-x7jpyRYsLE5X_FunoR_vV15/w640-h360/sid%208.png" title="Short Link Berhasil dibuat" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Short Link Berhasil dibuat</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Untuk mengganti link sesuai keinginan kita, klik tanda <b>pensil </b>di sebelah kanan link yang dibuat pada langkah diatas.</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7jTFP-FQgzdjnvpw-IfiRgtVUmLPfatZyUGXy2Iwvq39ChlLKTGLfWdd40e7lBXjqjXktJAJSmK2easlDviIE1rdStRrvnqRD8BT3jV0BXjkj4n5CmDpEPKjTZCe9jZZ82kHGmJyDkdo6CTPRKlXsfXWxvjF3nhRXALmc0IGViIIoWtmKPG_txx3A/s1366/sid%209.png" style="margin-left: auto; margin-right: auto;"><img alt="Mengganti nama short link" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7jTFP-FQgzdjnvpw-IfiRgtVUmLPfatZyUGXy2Iwvq39ChlLKTGLfWdd40e7lBXjqjXktJAJSmK2easlDviIE1rdStRrvnqRD8BT3jV0BXjkj4n5CmDpEPKjTZCe9jZZ82kHGmJyDkdo6CTPRKlXsfXWxvjF3nhRXALmc0IGViIIoWtmKPG_txx3A/w640-h360/sid%209.png" title="Mengganti nama short link" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Tool Mengganti Nama Short Link</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li><span style="font-size: medium;">Gantilah Nama sesuai dengan yang diinginkan</span></li><li><span style="font-size: medium;">Lalu klik <b>tanda centang</b>.</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX2vk26956fVYXYNwVNEkZDUUa42F8tj8alIRI4YlnN9Gvz0CXoxTFX8KAJiUQ6F2nzC7n0Uv_YnhnCVIhRGHYkgzF6tCwABPe_0X1_o4eAU2Lkqn8ar0ZthdYT4bV1XbtbOlMmHRCpOt9Bwljv5aA7ChN888Ln2gCS_a50_4aF4dCaoi_3poc_NGg/s1366/sid%2010.png" style="margin-left: auto; margin-right: auto;"><img alt="Mengganti nama short link" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX2vk26956fVYXYNwVNEkZDUUa42F8tj8alIRI4YlnN9Gvz0CXoxTFX8KAJiUQ6F2nzC7n0Uv_YnhnCVIhRGHYkgzF6tCwABPe_0X1_o4eAU2Lkqn8ar0ZthdYT4bV1XbtbOlMmHRCpOt9Bwljv5aA7ChN888Ln2gCS_a50_4aF4dCaoi_3poc_NGg/w640-h360/sid%2010.png" title="Mengganti nama short link" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Mengganti nama short link</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Untuk membagikan link, klik Tool <b>Share</b>, kemudian pilih link mau dibagi ke <b>facebook, twitter, whatsapp </b>dan lainya.</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAVaNXDAQMwbZmcOIhkbdtyUTLRJS6sn6dDzPU2K1K_NMjmzay2EhueHq2i51h1WFJuH6hz9tJcII6CzY2bO-Ab0atfstie-w6N-BP_tGZ3xlBWQl1xiTMCuNXXD-hENio0-9ZNTKKJkWT54NvKfU4AKOdzgIs0khKQioVpG5tBkCNZow6fYhcEFkP/s1366/sid%2011.png" style="margin-left: auto; margin-right: auto;"><img alt="Share link" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAVaNXDAQMwbZmcOIhkbdtyUTLRJS6sn6dDzPU2K1K_NMjmzay2EhueHq2i51h1WFJuH6hz9tJcII6CzY2bO-Ab0atfstie-w6N-BP_tGZ3xlBWQl1xiTMCuNXXD-hENio0-9ZNTKKJkWT54NvKfU4AKOdzgIs0khKQioVpG5tBkCNZow6fYhcEFkP/w640-h360/sid%2011.png" title="Share link" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 11. Share link</td></tr></tbody></table><br /><div><br /></div><h2 style="text-align: left;"><b><span style="font-size: medium;">MEMBUAT MICROSITE</span></b></h2><p style="text-align: left;"></p><ul style="text-align: left;"><li><span style="font-size: medium;">Dari halaman Dashboard klik menu <b>Microsite</b></span></li><li><span style="font-size: medium;">Klik tombol <b>+ Create new</b></span></li></ul><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsH7R-Cxp0-MHDPHF6OiyqRVvPm47m-PlM3IXXdXQrLcTYzPwo5XE2V9Qe9JgS29YBZbnSwc2x7vVf80YNpDf366ISmJhqHEd6qBQ0pv-A7zzsgW5qoxKRBkZLexk9tlAYeCZpj5izdkh0rR62YfCDnLmTKojPhnSHgvDNpZpxwIFXmNbMpgFBvdxE/s1366/sid%2012.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Microsite Baru" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsH7R-Cxp0-MHDPHF6OiyqRVvPm47m-PlM3IXXdXQrLcTYzPwo5XE2V9Qe9JgS29YBZbnSwc2x7vVf80YNpDf366ISmJhqHEd6qBQ0pv-A7zzsgW5qoxKRBkZLexk9tlAYeCZpj5izdkh0rR62YfCDnLmTKojPhnSHgvDNpZpxwIFXmNbMpgFBvdxE/w640-h360/sid%2012.png" title="Membuat Microsite Baru" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 12. Membuat Microsite Baru</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li><span style="font-size: medium;">Klik template yang diinginkan</span></li><li><span style="font-size: medium;">Jika ingin melihat klik <b>preview</b></span></li><li><span style="font-size: medium;">Tutup kotak <b>Preview</b></span></li><li><span style="font-size: medium;">Lalu klik tombol <b>Next</b></span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU2Ys023VzgEAKXyQPOLoJzLMFEOqto-CH-Pk1FMxrfvbSzg312XRfhCegPrt2PF6J-aE7v1_j75q2gePQsFMedU4N-zSuufSoEhpPHfyfVr1sviZs9_kodED6QHhIKHxkwQ3XeqhPMr7zWWU5jo6uAl4JwzNXMCYbl7D5vecrAnRj0YTL8gwoOKsb/s1366/sid%2014.png" style="margin-left: auto; margin-right: auto;"><img alt="Memilih templat" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU2Ys023VzgEAKXyQPOLoJzLMFEOqto-CH-Pk1FMxrfvbSzg312XRfhCegPrt2PF6J-aE7v1_j75q2gePQsFMedU4N-zSuufSoEhpPHfyfVr1sviZs9_kodED6QHhIKHxkwQ3XeqhPMr7zWWU5jo6uAl4JwzNXMCYbl7D5vecrAnRj0YTL8gwoOKsb/w640-h360/sid%2014.png" title="Memilih templat" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 14. Templat Microsite</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buatlah <b>Nama Microsite</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Buatlah <b>url (link)</b> dari microsite</span></li><li style="text-align: justify;"><span style="font-size: medium;">Pilih <b>tipe</b>, misal pendidikan</span></li><li style="text-align: justify;"><span style="font-size: medium;">Klik tombol <b>Create</b></span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6QpM4YROblo1CY8OamYAkvD4o0U0MDEi4925e1Wq-y9bl1sJeHi4J4ATiQJui2h49moJWBInkO_5YyvoDjCQlj-iwI_AeN-e1Nb411U3Zq3_wnX1vYxj1aI8IlNVW6tDNgGg0O5VKmOtO-cDYRLK_5-5EtlI-myG6tlyKEJaZOTQEKbWt7OayVQKT/s1366/sid%2015.png" style="margin-left: auto; margin-right: auto;"><img alt="Nama, alamat link dan tipe microsite" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6QpM4YROblo1CY8OamYAkvD4o0U0MDEi4925e1Wq-y9bl1sJeHi4J4ATiQJui2h49moJWBInkO_5YyvoDjCQlj-iwI_AeN-e1Nb411U3Zq3_wnX1vYxj1aI8IlNVW6tDNgGg0O5VKmOtO-cDYRLK_5-5EtlI-myG6tlyKEJaZOTQEKbWt7OayVQKT/w640-h360/sid%2015.png" title="Nama, alamat link dan tipe microsite" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 15. Nama, alamat link dan tipe microsite</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Microsite berhasil dibuat, tunggu sampai proses pemuatan halaman microsite selesai, maka kotak dibawah ini akan ditutup secara otomatis</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPOq2NazuhqwgUKYLxD_5Vy1ctIrJPIAeWclGRGmbcvWoLAQct0IYa7U2wt0xYA393ANZcyrdVBomG4GBZH3zW7-Pvqs1Z35A1bGtgO6MaQHLFHUWfoPsX9Bv65WV78_iDp0UsMrKoWKeGYUcSFwq0MWLzdHHz_Zmcc8MT50X93AFe6r_IrhlrLvgm/s1366/sid%2016.png" style="margin-left: auto; margin-right: auto;"><img alt="Microsite berhasil dibuat" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPOq2NazuhqwgUKYLxD_5Vy1ctIrJPIAeWclGRGmbcvWoLAQct0IYa7U2wt0xYA393ANZcyrdVBomG4GBZH3zW7-Pvqs1Z35A1bGtgO6MaQHLFHUWfoPsX9Bv65WV78_iDp0UsMrKoWKeGYUcSFwq0MWLzdHHz_Zmcc8MT50X93AFe6r_IrhlrLvgm/w640-h360/sid%2016.png" title="Microsite berhasil dibuat" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 16. Microsite berhasil dibuat</td></tr></tbody></table><br /><div><br /></div><h2 style="text-align: left;"><b><span style="font-size: medium;">MELAKUKAN PENGATURAN DAN MENAMBAH KOMPONEN MICROSITE</span></b></h2><p style="text-align: justify;"><span style="font-size: medium;">Tampilan Microsite sebelum melakukan pengaturan lanjutan. Gambar sebelah kiri merupakan layar kerja microsite, dan gambar sebelah kanan merupakan priview dari microsite</span></p><p style="text-align: left;"><span style="font-size: medium;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhhwO-EU2-qMQe6gFaNuA5muYDzaGxu2zqlvjtPZirw6Ym7SBmvzdFnOq9vzuKtxX0FPNpu4eBl8Zh_OvGYIDrlvXhoCy8_PK_tDtFzRnaerr6W2Pfx5GfsoXbr8NPWqfXCI_-DpQWbmdKpfjYQk1bfQ8Y4RdKhkSGQJZkhjwivMbLKuUIx0CVfBSNA" style="margin-left: auto; margin-right: auto;"><img alt="Tampilan Microsite MGMP" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhhwO-EU2-qMQe6gFaNuA5muYDzaGxu2zqlvjtPZirw6Ym7SBmvzdFnOq9vzuKtxX0FPNpu4eBl8Zh_OvGYIDrlvXhoCy8_PK_tDtFzRnaerr6W2Pfx5GfsoXbr8NPWqfXCI_-DpQWbmdKpfjYQk1bfQ8Y4RdKhkSGQJZkhjwivMbLKuUIx0CVfBSNA=w640-h360" title="Tampilan Microsite MGMP" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 17. Tampilan Microsite MGMP</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><h3 style="text-align: left;"><span style="font-size: medium;"><b>MENGUBAH KOMPONEN GAMBAR/LOGO</b></span></h3><p></p><div><ul style="text-align: left;"><li><span style="font-size: medium;">Sorot gambar logo</span></li><li><span style="font-size: medium;">Klik tanda pensil yang muncul</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfW4Yb_Jg4vletUNOKeRzAY8h4zHd4FkdwgCkelMyPvTmpPTxs8nLfop2_mYwd7Y_K5wJtk8kpqxij9sU6LT2Qe_fMK-DS7atFx02pbTl0-8jgvo4FwB3rJ_zd4fwv9SQpD5I2npvV32hhV8ad_NFCCqrp038nVAr03y9jhcjkv8FNwmLz6luQ8FMz/s1366/sid%2017.png" style="margin-left: auto; margin-right: auto;"><img alt="Mengganti Logo" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfW4Yb_Jg4vletUNOKeRzAY8h4zHd4FkdwgCkelMyPvTmpPTxs8nLfop2_mYwd7Y_K5wJtk8kpqxij9sU6LT2Qe_fMK-DS7atFx02pbTl0-8jgvo4FwB3rJ_zd4fwv9SQpD5I2npvV32hhV8ad_NFCCqrp038nVAr03y9jhcjkv8FNwmLz6luQ8FMz/w640-h360/sid%2017.png" title="Mengganti Logo" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 18. Mengganti Logo Microsite</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li><span style="font-size: medium;">Pilih lokasi gambar yang akan dijadikan logo</span></li><li><span style="font-size: medium;">Klik Open</span></li><li><span style="font-size: medium;">Tunggu beberapa saat sampai proses uploading gambar selesai</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkwQ-Z704L2tj93uLCWr_VlAMjLPxO7wL9wknb1bRCFwsIdJkUF8VUf_GTG84thU-WP87LD3YPYc9_rrUCGD6Jk5_22WyPvaNFtIbwlkHWjFry0aMPY3kVvK7Tgh-XS2t3Pjpa25RMVEsVUZXxBfN-hvXtj7cuCYdv8_fgUI7JlZk0ZENh8SULzxms/s1366/sid%2018.png" style="margin-left: auto; margin-right: auto;"><img alt="Mengganti Logo Microsite" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkwQ-Z704L2tj93uLCWr_VlAMjLPxO7wL9wknb1bRCFwsIdJkUF8VUf_GTG84thU-WP87LD3YPYc9_rrUCGD6Jk5_22WyPvaNFtIbwlkHWjFry0aMPY3kVvK7Tgh-XS2t3Pjpa25RMVEsVUZXxBfN-hvXtj7cuCYdv8_fgUI7JlZk0ZENh8SULzxms/w640-h360/sid%2018.png" title="Mengganti Logo Microsite" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 19. Mengganti Logo Microsite</td></tr></tbody></table><br /><div><br /></div><div><h3 style="text-align: justify;"><span style="font-size: medium;"><b>EDIT KOMPONEN TEXT</b></span></h3><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Scrol ke bawah, klik panah kebawah pada Text Hello, kemudian ganti Hello dengan Judul Microsite</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ubah Text Size dan Font Size sesuai yang diinginkan</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjv5RSx9lxIc9UqK_tShA17uSBLKsk-soyd559f89DLAYFibYkyrSrvx1mB2xuwmt2OlZPa-1l-aKWfaFTLnFC3cfwkWXymhRh7e9OPrIbYzPJfYm8tmbLR84-UN9qrSGwXFpTFmRnZkjw3cIU9jhWziNxkq08f_XSwhVmGXqgop09yQ778PAgda2OA/s1366/sid%2019.png" style="margin-left: auto; margin-right: auto;"><img alt="Edit Title Microsite" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjv5RSx9lxIc9UqK_tShA17uSBLKsk-soyd559f89DLAYFibYkyrSrvx1mB2xuwmt2OlZPa-1l-aKWfaFTLnFC3cfwkWXymhRh7e9OPrIbYzPJfYm8tmbLR84-UN9qrSGwXFpTFmRnZkjw3cIU9jhWziNxkq08f_XSwhVmGXqgop09yQ778PAgda2OA/w640-h360/sid%2019.png" title="Edit Title Microsite" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 20. Edit Title Microsite</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Dengan cara yang sama dengan cara diatas, ubah Text Welcome</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCJINPMxqY9rhTA3aAuDJF0lGb3GXIxmuOb4k64A_aysGrcd8EqfkdkjXE--KyPnIQj5cR5v6bBaQBdMsNEZKc__vz021PsrToz9B7n2meMIMIH74p6ju334L7nPr1RuPvCQddLQtjDxSLGXuT3AHKwVBtAMFWAhf7rxy59TodOVtKqyYpNODJulUg/s1366/sid%2020.png" style="margin-left: auto; margin-right: auto;"><img alt="Mengganti Text Welcome" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCJINPMxqY9rhTA3aAuDJF0lGb3GXIxmuOb4k64A_aysGrcd8EqfkdkjXE--KyPnIQj5cR5v6bBaQBdMsNEZKc__vz021PsrToz9B7n2meMIMIH74p6ju334L7nPr1RuPvCQddLQtjDxSLGXuT3AHKwVBtAMFWAhf7rxy59TodOVtKqyYpNODJulUg/w640-h360/sid%2020.png" title="Mengganti Text Welcome" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 21. Edit Text Welcome</td></tr></tbody></table><br /><div><br /></div><div><h3 style="text-align: left;"><span style="font-size: medium;"><b>EDIT KOMPONEN LINK</b></span></h3><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Edit Link : First Link. Klik panah ke bawah disampingnya</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ganti First Link dengan Judul Komponen, misal Surat Panggilan Peserta dan Jadwal Kegiatan</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ganti logo</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ubah pengaturan huruf jika diperlukan</span></li><li style="text-align: justify;"><span style="font-size: medium;">Masukkan link dokumen yang akan dilampirkan, misal link berbagi file di google drive. Disarankan untuk melakukan short link dari link berbagi google drive.</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5ImmQpGMajyjNOyd2D0_5gn00I981dR1xwgM6hHGndLxaGDVt-BUV3GH7KkdQXqRjTP-Rt03P1mIAwaC2YO0qZM7b0hMk-alDbB8pB73mIJTeOAllYl8Hbv74TKJa8s0Zml3e0hRSmkgADopAlgUPw9cz8zyKwPgQGOgHUbEqveaNElAiQ_GIOio2/s1366/sid%2021.png" style="margin-left: auto; margin-right: auto;"><img alt="Edit Komponen Link" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5ImmQpGMajyjNOyd2D0_5gn00I981dR1xwgM6hHGndLxaGDVt-BUV3GH7KkdQXqRjTP-Rt03P1mIAwaC2YO0qZM7b0hMk-alDbB8pB73mIJTeOAllYl8Hbv74TKJa8s0Zml3e0hRSmkgADopAlgUPw9cz8zyKwPgQGOgHUbEqveaNElAiQ_GIOio2/w640-h360/sid%2021.png" title="Edit Komponen Link" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 22. Edit Komponen Link</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Edit Link : Second Link, klik tanda panah ke bawah disampingnya</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ganti Second Link dengan Judul Komponen, misal Upload Surat Tugas</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ganti logo</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ubah pengaturan huruf jika diperlukan</span></li><li style="text-align: justify;"><span style="font-size: medium;">Masukkan link yang akan dilampirkan, misal link request file di One Drive untuk pengumpulan Surat Tugas. Cara membuat request file di One Drive dapat dipelajari melalui link <a href="https://www.nurmankarim.my.id/2022/03/request-file-di-onedrive.html" rel="nofollow" target="_blank">https://www.nurmankarim.my.id/2022/03/request-file-di-onedrive.html</a></span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyz5U8Lpx8fWFckADW8TH78o8bDjdQ4uC8MiNPGzjCVORNAxypdRaHZcQ0PatSpzYpKEZ23iYl2ohkZAiBG2bU7wJRQhuJzL_8Kz-4hsJyun4y6pwT8LIQvnix4akV2AfL6L-rUUKZs3qeMgC86raTK4TTDUoYwhhcznAH4iXgQ22jCsWtP1UXLgWE/s1366/sid%2022.png" style="margin-left: auto; margin-right: auto;"><img alt="Edit Komponen Second Link" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyz5U8Lpx8fWFckADW8TH78o8bDjdQ4uC8MiNPGzjCVORNAxypdRaHZcQ0PatSpzYpKEZ23iYl2ohkZAiBG2bU7wJRQhuJzL_8Kz-4hsJyun4y6pwT8LIQvnix4akV2AfL6L-rUUKZs3qeMgC86raTK4TTDUoYwhhcznAH4iXgQ22jCsWtP1UXLgWE/w640-h360/sid%2022.png" title="Edit Komponen Second Link" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 23. Edit Komponen Second Link</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li><span style="font-size: medium;">Edit Link : Last Link, klik tanda panah ke bawah disampingnya</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ganti Last Link dengan Judul Komponen, misal Upload Biodata</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ganti logo</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ubah pengaturan huruf jika diperlukan</span></li><li style="text-align: justify;"><span style="font-size: medium;">Masukkan link yang akan dilampirkan, misal link request file di One Drive untuk pengumpulan Biodata.</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2aQRe2-3z2yi0eqjwiWHO8SJZ6yIRw9PzjEQa9yBFUjgOJIvTW8G3xwlzWhip-DnSDTrboRnqfe3gryVoYwGyCK4wwqdAgO8Pqm3bN-b3_09fxo_7N-K94dLUekKVdXB4i0oo2YMj__SWoGtYULTWFSsYMjuh7zkEAau9bQ3PxKrrvy3DwnJysRa/s1366/sid%2023.png" style="margin-left: auto; margin-right: auto;"><img alt="Edit Last Link" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2aQRe2-3z2yi0eqjwiWHO8SJZ6yIRw9PzjEQa9yBFUjgOJIvTW8G3xwlzWhip-DnSDTrboRnqfe3gryVoYwGyCK4wwqdAgO8Pqm3bN-b3_09fxo_7N-K94dLUekKVdXB4i0oo2YMj__SWoGtYULTWFSsYMjuh7zkEAau9bQ3PxKrrvy3DwnJysRa/w640-h360/sid%2023.png" title="Edit Last Link" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 24. Edit Last Link</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Karena komponen yang disedikan template sudah habis, maka kita perlu untuk menambahkan komponen lagi.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Klik + Add New Component</span></li><li style="text-align: justify;"><span style="font-size: medium;">Klik Link</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCWiwGpmrtSXqH9EjIct0dOAoN9HkdIJ6tL8Qy9QABHolztQdAR-Ws2T-70glA1kzivtann8lYsLoTPmKoTXSDs3gCRrEwlE_Q-IPV55XdTJsDc4tKHW6-9kvZ96YI49yMKZbjJ-_1ft0ybReSFbG4e66EQzgjr2myqdzM-n_phqiXv5LbrxYaMGJv/s1366/sid%2024.png" style="margin-left: auto; margin-right: auto;"><img alt="Add New Component" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCWiwGpmrtSXqH9EjIct0dOAoN9HkdIJ6tL8Qy9QABHolztQdAR-Ws2T-70glA1kzivtann8lYsLoTPmKoTXSDs3gCRrEwlE_Q-IPV55XdTJsDc4tKHW6-9kvZ96YI49yMKZbjJ-_1ft0ybReSFbG4e66EQzgjr2myqdzM-n_phqiXv5LbrxYaMGJv/w640-h360/sid%2024.png" title="Add New Component" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 25. Add New Component</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Seperti pada langkah-langkah diatas isi dengan komponen materi Toleransi Dalam Keberagaman</span></li><li style="text-align: justify;"><span style="font-size: medium;">Selanjutnya buat, materi-materi yang lain</span></li><li style="text-align: justify;"><span style="font-size: medium;">Geser posisi komponennya ke bawah</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGpoNiT9eQsFYHTaRm_RNYIsdAT2Oy10-ctkR7BQPV2WymVYB6CM00Gas4Xe-i2_4NEs0_9FIQJfNSfZD9V95pwmY4YAwzwVO4GDuhJ6B2W3P5MW-L7TcpXxsmvK8TTS_xJRBiqmdzt40m0aMSsSwEgbdK97s98Ifyl_DB8w5mFQcTndQgI5NMh4RB/s1366/sid%2025.png" style="margin-left: auto; margin-right: auto;"><img alt="Menambah Komponen" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGpoNiT9eQsFYHTaRm_RNYIsdAT2Oy10-ctkR7BQPV2WymVYB6CM00Gas4Xe-i2_4NEs0_9FIQJfNSfZD9V95pwmY4YAwzwVO4GDuhJ6B2W3P5MW-L7TcpXxsmvK8TTS_xJRBiqmdzt40m0aMSsSwEgbdK97s98Ifyl_DB8w5mFQcTndQgI5NMh4RB/w640-h360/sid%2025.png" title="Menambah Komponen" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 26. Menambah Komponen</td></tr></tbody></table><br /><br /><h3 style="text-align: left;"><span style="font-size: medium;"><b>EDIT HORIZONTAL LINK</b></span></h3><p style="text-align: justify;"><span style="font-size: medium;">Fitur ini berfungsi untuk menyematkan link media sosial seperti Facebook, Youtube, Twitter, Website dan lainnya.</span></p><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Edit Horizotal Link. Klik tanda panah ke bawah disampingnya</span></li><li style="text-align: justify;"><span style="font-size: medium;">Copy link Media sosial anda.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Paste sesuai dengan media sosial yang ingin anda sematkan</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKyyR74CCNGW-mJynGFWV0h519ZrokETHYu6JqDsDJGeX3MnXzbilTNlZFDhA537X_cNnZZNQxE2X_mElk-iBg6S0A-ZLPcx9YrQCuqfM74C2rjkn0TVXevP-YUvVNdJEpWsIlBiEa3uEw8GeWkAYlCeLAumS2h_ubm89SgTI_FTkGc7W5xJmsje8H/s1366/sid%2026.png" style="margin-left: auto; margin-right: auto;"><img alt="Menyematkan link media sosial" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKyyR74CCNGW-mJynGFWV0h519ZrokETHYu6JqDsDJGeX3MnXzbilTNlZFDhA537X_cNnZZNQxE2X_mElk-iBg6S0A-ZLPcx9YrQCuqfM74C2rjkn0TVXevP-YUvVNdJEpWsIlBiEa3uEw8GeWkAYlCeLAumS2h_ubm89SgTI_FTkGc7W5xJmsje8H/w640-h360/sid%2026.png" title="Menyematkan link media sosial" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 27. Menyematkan link media sosial</td></tr></tbody></table><br /><p style="text-align: justify;"><span style="font-size: medium;">Hasil dari Microsite diatas seperti gambar berikut. Jika ingin melihat versi smart phone silahkan klik gambar tersebut.</span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://s.id/mgmpmathntb2022" rel="nofollow" target="_blank"><img alt="Tampilan Versi Smart Phone" border="0" data-original-height="1280" data-original-width="590" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoh2dFONdG_dUJRQ6tYY6II9t1_FAF5SFTWD66YluRKNcTTtths2ciyW2gTRbzoYmYl5TIGDiZhNIfljrZu3OFflaIQyecaP0RaGBlif7BOdEwtJCH2cuuyMXoQ1s2aFssqYtdQD2M3UbTsT_wP68SYlxsaTKxvS8ekMA-C0UEhZyxx9YaBYUhTLn2/w296-h640/WhatsApp%20Image%202022-10-03%20at%2021.28.29.jpeg" title="Tampilan Versi Smart Phone" width="296" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://s.id/mgmpmathntb2022" rel="nofollow" target="_blank">Gambar 28. Tampilan Versi Smart Phone</a></td></tr></tbody></table><br /><br /><p style="text-align: justify;"><span style="font-size: large;">Demikian pembahasan langkah-langkah membuat microsite di Shortlink s.id. Semoga bermanfaat. terimakasih.</span></p><p></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-57763864722578092932022-10-02T16:03:00.005+08:002022-11-11T09:53:25.088+08:00Cara Menentukan Nilai sin, cos, tan Tanpa Menggunakan Tabel dan Kalkulator <p style="text-align: justify;"><b style="font-size: large;"></b></p><span style="font-size: medium;"><div style="text-align: justify;"><b><div class="separator" style="clear: both; text-align: center;"><b style="text-align: justify;">Cara Menentukan Nilai sin, cos, tan Tanpa Menggunakan Tabel dan Kalkulator -</b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgy87ykyPjrU1vPpy_DJjZUYr5qXb7JgiKPxzdcuzF0Rx--k-WQYmle12q_NC7GGbADSilXRXvQuRclEbirgyxmxmKhNIC_RsHfHPVDCQ-p0wq70Bkf7BSja9J3So1wkgn7BOcqS5CCQqtU4NHL6DCNNfOic1BmIeJnPiszkQyMNJhdlTDtu_CvE6x/s600/sudut%201-1.png" style="margin-left: 1em; margin-right: 1em;"><img alt="Menentukan nilai sudut dengan busur derajat" border="0" data-original-height="600" data-original-width="600" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgy87ykyPjrU1vPpy_DJjZUYr5qXb7JgiKPxzdcuzF0Rx--k-WQYmle12q_NC7GGbADSilXRXvQuRclEbirgyxmxmKhNIC_RsHfHPVDCQ-p0wq70Bkf7BSja9J3So1wkgn7BOcqS5CCQqtU4NHL6DCNNfOic1BmIeJnPiszkQyMNJhdlTDtu_CvE6x/w200-h200/sudut%201-1.png" style="float: left; margin: 5px 9px;" title="Menentukan nilai sudut dengan busur derajat" width="200" /></a></div></b> Pada pembelajaran Trigonometri seringkali seorang guru mengkondisikan soal supaya mendapatkan sudut istimewa sehingga nilai sin x, cos x, tan x atau yang lain dengan cepat bisa dihitung. Tetapi bagaimana jika kita mendapatkan bukan sudut istimewa, tentunya siswa diarahkan untuk melihat tabel atau menggunakan kalkulator, PC atau Laptop.</div></span><p></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Misal</span></p>
<p style="text-align: center;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?sin&space;145^{\circ&space;}=sin&space;(180^{\circ}&space;-35^{\circ&space;})=sin&space;35^{\circ&space;}" title="https://latex.codecogs.com/svg.image?sin 145^{\circ }=sin (180^{\circ} -35^{\circ })=sin 35^{\circ }" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena <img src="https://latex.codecogs.com/svg.image?35^{\circ&space;}" title="https://latex.codecogs.com/svg.image?35^{\circ }" /> bukan merupakan sudut istimewa maka jika mau menentukan nilai dari <img src="https://latex.codecogs.com/svg.image?sin35^{\circ&space;}" title="https://latex.codecogs.com/svg.image?sin35^{\circ }" /> harus menggunakan tabel atau kalkulator maupun laptop.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Nah, sekarang bagaimanakah cara menentukan nilai sin, cos, tan dan lainnya jika sudutnya bukan merupakan sudut istimewa. Misal kita ingin menentukan nilai dari <img src="https://latex.codecogs.com/svg.image?sin35^{\circ&space;}" title="https://latex.codecogs.com/svg.image?sin35^{\circ }" /> diatas.</span></p><h2 style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah menentukan nilai sin, cos dan tan</span></h2><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah menentukan nilai sin, cos dan tan tanpa menggunakan tabel dan kalkulator.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Alat dan Bahan</b></span></p><p style="text-align: justify;"></p><ol><li><span style="font-size: medium;">Pensil atau Polpen</span></li><li><span style="font-size: medium;">kertas milimeter, jika tidak ada bisa menggunakan kertas biasa</span></li><li><span style="font-size: medium;">Busur derajat</span></li><li><span style="font-size: medium;">Penggaris</span></li></ol><span style="font-size: medium;"><b>Langkah-langkah</b></span><p></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Buat sumbu koodinat kartesius pada kertas yang sudah disediakan</span></li><li><span style="font-size: medium;">Ukurlah sudut <img src="https://latex.codecogs.com/svg.image?35^{\circ&space;}" title="https://latex.codecogs.com/svg.image?35^{\circ }" /> menggunakan busur derajat</span></li></ul><span style="font-size: medium;"><div style="text-align: center;"><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGhZQ4fHcbePPmAyCub1v49OBWaFThTcoU6-GQ4Riwgn2TR7Bmv56h7UVujx7-d-Po3TmFYJBBm2FBQa3SHtJtfgPx-5Bldl7p5tM9YZCqWvfrry9f3gCDsPmtj_ULx-J3JfPxTWSS5pNQWWH0emTbjnAmg6Zzs0NViyKUIF9ktIt-7NX0Km5kFsS4/s600/sudut%201-1.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGhZQ4fHcbePPmAyCub1v49OBWaFThTcoU6-GQ4Riwgn2TR7Bmv56h7UVujx7-d-Po3TmFYJBBm2FBQa3SHtJtfgPx-5Bldl7p5tM9YZCqWvfrry9f3gCDsPmtj_ULx-J3JfPxTWSS5pNQWWH0emTbjnAmg6Zzs0NViyKUIF9ktIt-7NX0Km5kFsS4/s320/sudut%201-1.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 1. Mengukur Sudut <img src="https://latex.codecogs.com/svg.image?35^{\circ&space;}" style="text-align: justify;" title="https://latex.codecogs.com/svg.image?35^{\circ }" /> menggunakan busur derajat</span></td></tr></tbody></table></td></tr></tbody></table><p></p></div></span><div><ul><li style="text-align: justify;"><span style="font-size: medium;">Buatlah garis dengan panjang 10 cm dari pusat koodinat ke titik yang diperoleh dari langkah diatas. (<i>Perhatikan panjang garis 10 cm hanya untuk memudahkan perhitungan, bisa juga menggunakan ukuran panjang lain</i>)</span></li></ul><p style="text-align: left;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiAMufAUKxr6md3XJalBTL_NzBHCa5gVmSdiCbu4eSZdxV6L1lG9A0MDY3xkL3WwH9N-gsRyKB4dE93Qs8ndGr2hCqAT9fNAM7VD67yVKM7u5uGVYvMWReAyT_Nq1FCgsofpocBHLo1s8CoanQY_TdfabB-_BauebbXmnQb2SglSYnq131gaxF4WR8/s400/sudut%202-1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Membuat garis dari titik sudut" border="0" data-original-height="400" data-original-width="400" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiAMufAUKxr6md3XJalBTL_NzBHCa5gVmSdiCbu4eSZdxV6L1lG9A0MDY3xkL3WwH9N-gsRyKB4dE93Qs8ndGr2hCqAT9fNAM7VD67yVKM7u5uGVYvMWReAyT_Nq1FCgsofpocBHLo1s8CoanQY_TdfabB-_BauebbXmnQb2SglSYnq131gaxF4WR8/w400-h400/sudut%202-1.png" title="Membuat garis dari titik sudut" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Membuat garis dengan panjang 10 cm dari titik sudut</td></tr></tbody></table></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Tarik garis dari Ujung garis diatas ke sumbu horizontal, lihat dan catat panjangnya</span></li></ul><p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtAbhSqhDn4d8OwaYnpz_P62JcLrT84vMYUJLbXQqPmULapuN2kWAFK32Vlfl9OXVKGRUeb5gqpBlarwG0VclZzlbC_uwTaEKw0lteMOydytKXcr0TWlD9BZe2ZcmxqV9ISb5KggZnxVd8jRi4p_olfRZIBkXeEFuAaO7wp7k192B00RBoSbn_Z2vC/s400/sudut%203-1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Mengukur panjang garis vertikal" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtAbhSqhDn4d8OwaYnpz_P62JcLrT84vMYUJLbXQqPmULapuN2kWAFK32Vlfl9OXVKGRUeb5gqpBlarwG0VclZzlbC_uwTaEKw0lteMOydytKXcr0TWlD9BZe2ZcmxqV9ISb5KggZnxVd8jRi4p_olfRZIBkXeEFuAaO7wp7k192B00RBoSbn_Z2vC/s16000/sudut%203-1.png" title="Mengukur panjang garis vertikal" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 3. Membuat garis dari ujung garis sudut ke sumbu horizontal</span></td></tr></tbody></table></td></tr></tbody></table></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Ukurlah panjang garis dari pusat koordinat ke garis vertikal yang dibuat dari langkah diatas atas. Jangan lupa ditulis ukurannya.</span></li></ul><ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4n28o95XBA3AYTZDvx5wL-YH90HS2HD5ZUaYjJXxmrv4s3A6ZIPVevvbqin5dBoOrimZSgCdXxnSm7-dIP3knemsPOCPaR4zLh9KcV679XO-Wj4Imm-q3tNQYxCzplk3fegRFhyMjQ1ojX3baWNEx2XG7dmrE0gCAlEIU-Jo5KwWO8wWC_uCDx2Pw/s600/Sudut%204-1.png" style="margin-left: auto; margin-right: auto;"><img alt="Gambar 4. Mengukur panjang garis dari sumbu koordinat ke garis vertikal" border="0" data-original-height="600" data-original-width="600" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4n28o95XBA3AYTZDvx5wL-YH90HS2HD5ZUaYjJXxmrv4s3A6ZIPVevvbqin5dBoOrimZSgCdXxnSm7-dIP3knemsPOCPaR4zLh9KcV679XO-Wj4Imm-q3tNQYxCzplk3fegRFhyMjQ1ojX3baWNEx2XG7dmrE0gCAlEIU-Jo5KwWO8wWC_uCDx2Pw/s16000/Sudut%204-1.png" title="Gambar 4. Mengukur panjang garis dari sumbu koordinat ke garis vertikal" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 4. Mengukur panjang garis dari sumbu koordinat ke garis vertikal</span></td></tr></tbody></table></td></tr></tbody></table></ul><p></p><p style="text-align: left;"></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Dengan menggunakan rumus perbandingan trigonometri hitunglah nilai <img src="https://latex.codecogs.com/svg.image?sin35^{\circ&space;}" style="text-align: justify;" title="https://latex.codecogs.com/svg.image?sin35^{\circ }" /> dan nilai trigonomteri lainnya.</span></li></ul><p style="text-align: left;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxwSYU96XbzAwz4CoTkwbnLx7dyKoi0GCMxIccmLhn5_pP2g4VhA48jLT9QHwL9z4BqzSwtGT42GlF3RPH5M4dP6FpuR_hfp0XgJj8d577KoYwtZ8FdAXzw6ppCStRDLURSAeg_hPZaRCMFQv0mlCqgGjDtunOBl2LnO3sbiprLky7_QICSthTuu_d/s400/sudut%204-1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Menghitung nilai sin, cos, dan tan" border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxwSYU96XbzAwz4CoTkwbnLx7dyKoi0GCMxIccmLhn5_pP2g4VhA48jLT9QHwL9z4BqzSwtGT42GlF3RPH5M4dP6FpuR_hfp0XgJj8d577KoYwtZ8FdAXzw6ppCStRDLURSAeg_hPZaRCMFQv0mlCqgGjDtunOBl2LnO3sbiprLky7_QICSthTuu_d/s16000/sudut%204-1.png" title="Menghitung nilai sin, cos, dan tan" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Menghitung nilai sin, cos dan tan</td></tr></tbody></table></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Untuk meyakinkan hasilnya silahkan bandingkan dengan hasil perhitungan menggunakan kalkulator atau laptop.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Silahkan dicoba untuk ukuran sudut yang lain.</span></li></ul><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="font-size: medium;">Demikian langkah-langkah cara menentukan nilai sin, cos, tan tanpa menggunakan tabel dan kalkulator, Pada kesempatan ini saya sampaikan terimakasih kepada kawan-kawan satu team Fasilitator Refreshment Fasilitator Daerah PKB Matematika MA Zona 1 Kelas MAT A yang telah memberikan pembelajaran materi ini kepada penulis. Semoga tulisan ini bermanfaat untuk kemajuan pembelajaran Matematika. Terimakasih.</span></div></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-5724228640007637662022-10-01T14:05:00.002+08:002022-10-31T17:29:11.273+08:00Menggunakan Aplikasi Geogebra Pada Matriks<h2 style="text-align: justify;"><span style="font-size: medium;"><b>Menggunakan Aplikasi Geogebra Pada Matriks</b></span></h2><p style="text-align: justify;"><span style="font-size: medium;">Materi Matriks bagi sebagian siswa dianggap materi yang tidak sulit, dan sebagiannya lagi tetap beranggapan semudah apapun materi matematika tetap dianggap sulit. Untuk membantu para siswa untuk melakukan perhitungan pada operasi matriks yang dapat dijadikan pedoman untuk perhitungan manual, berikut saya berikan langkah-langkah menggunakan aplikasi geogebra pada matriks.</span></p><h3 style="text-align: justify;"><span style="font-size: medium;"><b>PERSIAPAN</b></span></h3><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Buka aplikasi Geogebra</span></li><li><span style="font-size: medium;">Klik <b><span style="color: red;">Garis Tiga</span></b></span></li><li><span style="font-size: medium;">Klik <b><span style="color: red;">Tampilan</span></b></span></li><li><span style="font-size: medium;">Centang kotak <b><span style="color: red;">Tampilan Ajabar</span></b> dan <span style="color: red;"><b>Tampilan Spreadsheet</b></span></span></li><li><span style="font-size: medium;">Untuk menghilangkan tampilan kotak garis tiga klik diluar kotak</span></li></ul><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihzsYErTb1uXGUNmikbLnVZnWdCuZbexTvKGU28fq1Vp8sXYgjkDq_oEN1-mdDyBnHMkNU5w9OlDAU4A132-xY2xI9SdofGXNtYj9BPxLbA-SCyP_gVuoCMQEuxmoGV7dCOGI2mYOd-CFHWiOrVfvZ8cr262NH5j5PuZBdybGYJm198XtMGJZWQEsS/s1366/geogebra%2024.png" style="margin-left: auto; margin-right: auto;"><img alt="Aplikasi geogebra spreadsheet" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihzsYErTb1uXGUNmikbLnVZnWdCuZbexTvKGU28fq1Vp8sXYgjkDq_oEN1-mdDyBnHMkNU5w9OlDAU4A132-xY2xI9SdofGXNtYj9BPxLbA-SCyP_gVuoCMQEuxmoGV7dCOGI2mYOd-CFHWiOrVfvZ8cr262NH5j5PuZBdybGYJm198XtMGJZWQEsS/w640-h360/geogebra%2024.png" title="Aplikasi geogebra spreadsheet" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Tampilan Aljabar dan Tampilan Spreadsheet aplikasi Geogebra</td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Misal kita akan selesaikan soal berikut.</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Diketahui Matriks </span><img src="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}14&space;&&space;18&space;&&space;17&space;\\13&space;&&space;10&space;&&space;15&space;\\12&space;&&space;11&space;&&space;12&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?A=\begin{pmatrix}14 & 18 & 17 \\13 & 10 & 15 \\12 & 11 & 12 \\\end{pmatrix}" />, dan<span style="text-align: left;"> </span><img src="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}10&space;&&space;12&space;&&space;15&space;\\10&space;&&space;5&space;&&space;10&space;\\11&space;&&space;9&space;&&space;11&space;\\\end{pmatrix}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?B=\begin{pmatrix}10 & 12 & 15 \\10 & 5 & 10 \\11 & 9 & 11 \\\end{pmatrix}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Hitunglah : A + B, A - B, B - A, A x B, B x A, Transpose A, Determinan A, Invers A, Invers AB</span></p><h3 style="text-align: justify;"><span style="font-size: medium;"><b>Langkah-langkah menghitung Transpose, Determinan dan Invers Matriks</b></span></h3><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Pada layar Spreadsheet isikan nilai-nilai pada sel matriks A</span></li><li><span style="font-size: medium;"><b>Blok semua sel</b> yang memuat nilai-nilai matriks A</span></li><li><span style="font-size: medium;">Klik kanan, klik/Sorot <b><span style="color: red;">+ Buat</span></b>, lalu klik <b><span style="color: red;">Matriks</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6dXHLzzfRjxpxCY2mfzCIF75_xcAYhrQVm95TtrWt3YAmlhXzXwsnJeoSpDF1_MoRbBa6WmKE47j8mlplEcLXHvzOc3fT0EbtyfISZTtDrQ1PncsPJb5jEl0CPCL_1Jz13BvfJaY3Df_EvwCZs4CcEqd9q8Ceni9IVdVy5-TIvCk0hlXmwpYYu1kT/s1366/geogebra%2025.png" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Matrik di Geogebra" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6dXHLzzfRjxpxCY2mfzCIF75_xcAYhrQVm95TtrWt3YAmlhXzXwsnJeoSpDF1_MoRbBa6WmKE47j8mlplEcLXHvzOc3fT0EbtyfISZTtDrQ1PncsPJb5jEl0CPCL_1Jz13BvfJaY3Df_EvwCZs4CcEqd9q8Ceni9IVdVy5-TIvCk0hlXmwpYYu1kT/w640-h360/geogebra%2025.png" title="Membuat Matrik di Geogebra" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Membuat Matriks di Aplikasi Geogebra</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><ul><li><span style="font-size: medium;">Diperoleh Matriks m1</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhDuCERaFrT39TZEDwYmJzpyqutupphozms9FhJArKBmk6a5ClF2dSQkHA78YstK8QBDmI4a365PSEvnAzrpRRaxXmCRQp00b_ylDrSrWj_X98fxxfddzJZbLe1TxvlXW4QK6UEOzSNEEmYrp83Lup5DYMYK1N9XK3t2ZioPjV-5f3D6yO-5EFc5lfc" style="margin-left: auto; margin-right: auto;"><img alt="Matriks A ordo 3 x 3" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhDuCERaFrT39TZEDwYmJzpyqutupphozms9FhJArKBmk6a5ClF2dSQkHA78YstK8QBDmI4a365PSEvnAzrpRRaxXmCRQp00b_ylDrSrWj_X98fxxfddzJZbLe1TxvlXW4QK6UEOzSNEEmYrp83Lup5DYMYK1N9XK3t2ZioPjV-5f3D6yO-5EFc5lfc=w640-h360" title="Matriks A ordo 3 x 3" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Matriks m1 dengan ordo 3x3</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Ganti nama matriks m1 menjadi matriks A. Klik kanan di matriks m1, Klik Namai Ulang, Ganti m1 menjadi A, lalu Klik tombol OK</span></li><li style="text-align: justify;"><span style="font-size: medium;">Lakukan langkah-langkah diatas untuk membuat matriks B</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjvvsLXfZLqcbh1RnAKR_t4ZTTJutKgJ7IsVjrwn-QqSlB3ZLcvNMFTcMto1Xb5C6m3AfKKNgePZ94tDRS4sAGzUI1BcAWNV9gxvxpVdmeOrzOqmyMamnk1xscB_e0V7dG0SIgwoH_wbvtDHL9CC3RA73HdQaU1Mib69Tq8_9qQkxg8iUb1lDwKecEv" style="margin-left: auto; margin-right: auto;"><img alt="Matriks B dengan ordo 3x3" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjvvsLXfZLqcbh1RnAKR_t4ZTTJutKgJ7IsVjrwn-QqSlB3ZLcvNMFTcMto1Xb5C6m3AfKKNgePZ94tDRS4sAGzUI1BcAWNV9gxvxpVdmeOrzOqmyMamnk1xscB_e0V7dG0SIgwoH_wbvtDHL9CC3RA73HdQaU1Mib69Tq8_9qQkxg8iUb1lDwKecEv=w640-h360" title="Matriks B dengan ordo 3x3" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Matriks B Ordo 3x3</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Menghitung hasil dari A + B</span></li><li><span style="font-size: medium;">Pada kotak Masukkan ketik <b><span style="color: red;">A+B</span></b>, lalu tekan tombol Enter. Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgMJ0GuY9Em_NreHwT59rcvXU0GrAm1A5ZmN2S82F_IULB75XLYNi5RGO5tvRrcSluXqRM9ILq5_gVS4RUJoYM65D02mytP3MGyo7m9G4-Buk9msuuYaDsDr6Fv_YXLFmU6Zpy3z_j1Ptgk_ZSfwhCbdqptFmyL9h9QdFyXDRe_0P2b-ndhv2B3H9Fq" style="margin-left: auto; margin-right: auto;"><img alt="Operasi Penjumlahan Matriks A + B" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgMJ0GuY9Em_NreHwT59rcvXU0GrAm1A5ZmN2S82F_IULB75XLYNi5RGO5tvRrcSluXqRM9ILq5_gVS4RUJoYM65D02mytP3MGyo7m9G4-Buk9msuuYaDsDr6Fv_YXLFmU6Zpy3z_j1Ptgk_ZSfwhCbdqptFmyL9h9QdFyXDRe_0P2b-ndhv2B3H9Fq=w640-h360" title="Operasi Penjumlahan Matriks A + B" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Operasi Penjumlahan Matriks A + B</td></tr></tbody></table><br /><p></p><ul style="text-align: justify;"><li><span style="font-size: medium;">Menghitung hasil dari A - B</span></li><li><span style="font-size: medium;">Pada kotak Masukkan ketik<b style="color: red;"> A-B</b>, lalu tekan tombol Enter. Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEigM9TDlmJi__nqFVM8hUd4P9PMueJP-9mxZNOE4EXEn5oz5UlLHwn5i993dXPXnt5sM0LHf70nQoDgxrcj77ifoOigr2ctIS6UD-5QJpguGVUO-9VHRlt6TmQ7fhzaUeozpCk0qwQbbFRckCeu9GrxGsROcrp8QbI8dIIiB2Tpi-lk5qbQyrZutS87" style="margin-left: auto; margin-right: auto;"><img alt="Operasi Pengurang Matriks A-B" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEigM9TDlmJi__nqFVM8hUd4P9PMueJP-9mxZNOE4EXEn5oz5UlLHwn5i993dXPXnt5sM0LHf70nQoDgxrcj77ifoOigr2ctIS6UD-5QJpguGVUO-9VHRlt6TmQ7fhzaUeozpCk0qwQbbFRckCeu9GrxGsROcrp8QbI8dIIiB2Tpi-lk5qbQyrZutS87=w640-h360" title="Operasi Pengurang Matriks A-B" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Operasi Pengurang Matriks A-B</td></tr></tbody></table><br /><ul style="text-align: left;"><li><span style="font-size: medium;">Menghitung hasil dari A x B</span></li><li style="text-align: justify;"><span style="font-size: medium;">Pada kotak Masukkan <b><span style="color: red;">ketik A*B</span></b>, lalu tekan tombol Enter, (<i>Perhatikan untuk operasi kali gunakan tanda bintang</i>). Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiyJaUabJZrSKJvuB-Cl0nryMUHmBEvat5fCSFu8yx8xl6sw6EQbw8Z6y5X0vJoKAy4Iqe0r02grSjWx09pyfA3vHbClUZ9mp5Gjs8kTysNx847s-lwFlpWrfGnlQ3dypacMi6w_21JgJE5-A56dDPVMe9yAwAQwG_1lwv0NVjivYy775BwXFe918tT" style="margin-left: auto; margin-right: auto;"><img alt="Operasi Matriks A x B" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiyJaUabJZrSKJvuB-Cl0nryMUHmBEvat5fCSFu8yx8xl6sw6EQbw8Z6y5X0vJoKAy4Iqe0r02grSjWx09pyfA3vHbClUZ9mp5Gjs8kTysNx847s-lwFlpWrfGnlQ3dypacMi6w_21JgJE5-A56dDPVMe9yAwAQwG_1lwv0NVjivYy775BwXFe918tT=w640-h360" title="Operasi Matriks A x B" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Operasi Matriks A x B</td></tr></tbody></table><br /><ul style="text-align: left;"><li><span style="font-size: medium;">Menentukan Transpose Matriks A</span></li><li style="text-align: justify;"><span style="font-size: medium;">Pada kotak Masukkan <b><span style="color: red;">transpos(A)</span></b>, lalu tekan tombol Enter, Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgW9zgwZWExImpO9UAxHA6ut-B-RY7nAklcF2hgitd3QsV-grIZhxEGOybHoDmrmw8zNzhbMQm-bC-MxZ772Jowudv8HhgpNUU4AkkQxKVpJmybXH8Sx8JYkl9owwu3uNyh3ouXbmu2qol9TfSN-9m-PkRINZoQaZn-s04V--Crt750eFoQH0f8aEDa" style="margin-left: auto; margin-right: auto;"><img alt="Tanspose Matriks A" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgW9zgwZWExImpO9UAxHA6ut-B-RY7nAklcF2hgitd3QsV-grIZhxEGOybHoDmrmw8zNzhbMQm-bC-MxZ772Jowudv8HhgpNUU4AkkQxKVpJmybXH8Sx8JYkl9owwu3uNyh3ouXbmu2qol9TfSN-9m-PkRINZoQaZn-s04V--Crt750eFoQH0f8aEDa=w640-h360" title="Tanspose Matriks A" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Tanspose Matriks A</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Menentukan Transpose Matriks B</span></li><li style="text-align: justify;"><span style="font-size: medium;">Pada kotak Masukkan <b><span style="color: red;">transpos(B)</span></b>, lalu tekan tombol Enter, Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj_b8ETEAiPs6Y5_9SPCohFyL2tlc4CUvhBLTfwErjU5_eInudkJQz2nJ6eDvybcjMi52I-azycUOqIHarqIBFGRwxpBFy1jfl94qVDKOnB7RjmcdQt0s8m1iU5bvIRfOxroA9u6sFScNVBsdxbsBUrso_tEroE36EFT0hkIfbyaNHB6dd8goPLW6xU" style="margin-left: auto; margin-right: auto;"><img alt="Transpose Matriks B" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEj_b8ETEAiPs6Y5_9SPCohFyL2tlc4CUvhBLTfwErjU5_eInudkJQz2nJ6eDvybcjMi52I-azycUOqIHarqIBFGRwxpBFy1jfl94qVDKOnB7RjmcdQt0s8m1iU5bvIRfOxroA9u6sFScNVBsdxbsBUrso_tEroE36EFT0hkIfbyaNHB6dd8goPLW6xU=w640-h360" title="Transpose Matriks B" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Transpose Matriks B</td></tr></tbody></table><br /><ul style="text-align: left;"><li><span style="font-size: medium;">Menghitung Determinan Matriks A</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ketik <b><span style="color: red;">determinan(A)</span></b>, lalu tekan tombol Enter. Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgOlRE7uoo0O708780kRq0gaNGdGKhfOK7jxj-NmevN0RbPIlopZzRg2NAkxAwiFn8ivyyjBKWzHrvesEYyqTfQ-29YnCCqfIph7_wlyykzxcLVgaUgmt3g5rNyu9AU7nBzFuY7VF33S5SaAs6zmMjdcyleKY5FuAoqM-aqpkPYsfTn5OsvcO7Muk6N" style="margin-left: auto; margin-right: auto;"><img alt="Determinan Matriks A" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgOlRE7uoo0O708780kRq0gaNGdGKhfOK7jxj-NmevN0RbPIlopZzRg2NAkxAwiFn8ivyyjBKWzHrvesEYyqTfQ-29YnCCqfIph7_wlyykzxcLVgaUgmt3g5rNyu9AU7nBzFuY7VF33S5SaAs6zmMjdcyleKY5FuAoqM-aqpkPYsfTn5OsvcO7Muk6N=w640-h360" title="Determinan Matriks A" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Determinan Matriks A</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Menghitung Invers Matriks A</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ketik <b><span style="color: red;">invers(A)</span></b>, lalu tekan tombol Enter. Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjxM8_3PXkms5WbTdYLz3jBYAoSciJ_Lbk7PROCLYsOHIjssCSP1Q3ilYJfS6uPLdmODcgPeZKvoIx6ufMankcEVMIGZ3Z98kBdEWqCwdOr-XYXA99hGdVWwG6zXx0Tl7o6ejjYw8RbXNINkZ7mCyZ5M0NQ0Zb3eDRXB6dvyTE9CtnjLR_vAzhNutAv" style="margin-left: auto; margin-right: auto;"><img alt="Invers Matriks A" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjxM8_3PXkms5WbTdYLz3jBYAoSciJ_Lbk7PROCLYsOHIjssCSP1Q3ilYJfS6uPLdmODcgPeZKvoIx6ufMankcEVMIGZ3Z98kBdEWqCwdOr-XYXA99hGdVWwG6zXx0Tl7o6ejjYw8RbXNINkZ7mCyZ5M0NQ0Zb3eDRXB6dvyTE9CtnjLR_vAzhNutAv=w640-h360" title="Invers Matriks A" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 11. Invers Matriks A</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Menghitung Invers Matriks B</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ketik <b><span style="color: red;">invers(B)</span></b>, lalu tekan tombol Enter. Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEijK5ssVwM7e8gJRFelIFN_r2-GBFHDVtchcoywOMhyUQ2tbfnSKLuXBBTMkiJdoGJoo7z5NnBSB05xzVr5Chx9ypf805j1GsdPOtnqNkmBo-tpmT3vRBnHHQw6JVO8IZmulrAxT7ueieOmTTs7uPTrVaErYqd1BpWxqFPyA-NPJzS_zV9yrk5e6BZk" style="margin-left: auto; margin-right: auto;"><img alt="Invers Matriks B" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEijK5ssVwM7e8gJRFelIFN_r2-GBFHDVtchcoywOMhyUQ2tbfnSKLuXBBTMkiJdoGJoo7z5NnBSB05xzVr5Chx9ypf805j1GsdPOtnqNkmBo-tpmT3vRBnHHQw6JVO8IZmulrAxT7ueieOmTTs7uPTrVaErYqd1BpWxqFPyA-NPJzS_zV9yrk5e6BZk=w640-h360" title="Invers Matriks B" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 12. Invers Matriks B</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Menghitung Invers Matriks AB</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ketik <b><span style="color: red;">invers(A*B)</span></b>, lalu tekan tombol Enter. Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhhAkZ8u2vnTefpw2nBcvzP2ywVTzhuKzk6fZ0zM6pHckKigwQxeeSEPa6VWvVI_UtgubIZMBylg8KlwIMTy7XO3jc-gF6M2221CPZ6W-6xJKRzshoNBC5W-iPX3S6n1E0KpVplbfBwQnSR2ErY9aqVLIhPLfqPSxLk7HJcirmWQpC3z9jHuvA3KZNe" style="margin-left: auto; margin-right: auto;"><img alt="Invers Matriks AB" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhhAkZ8u2vnTefpw2nBcvzP2ywVTzhuKzk6fZ0zM6pHckKigwQxeeSEPa6VWvVI_UtgubIZMBylg8KlwIMTy7XO3jc-gF6M2221CPZ6W-6xJKRzshoNBC5W-iPX3S6n1E0KpVplbfBwQnSR2ErY9aqVLIhPLfqPSxLk7HJcirmWQpC3z9jHuvA3KZNe=w640-h360" title="Invers Matriks AB" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 13. Invers Matriks AB</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Menghitung 2A-B+TransposA-Invers Matriks A</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ketik <b><span style="color: red;">2*A-B+transpos(A)-invers(A)</span></b> lalu tekan tombol Enter. Hasilnya seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgqZSrMD7GnFqtMhQ8t1nIQC9BsTcYDRp4QD2WhzxW9jke6jbsva3N5bMM_Q5zu6ak_qnCdjc0QG0UmcJ7wlTXIiLAQP5tw5qnj7hDoKQ9W_sxkRil32W11tM0p_50PtnUJRAhzNXppFmuxhWZJKA4_uxj6ulLogxMiR8uy_4YYMV56V_esFo6n-3lq" style="margin-left: auto; margin-right: auto;"><img alt="Operasi Campuran Pada Matriks" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgqZSrMD7GnFqtMhQ8t1nIQC9BsTcYDRp4QD2WhzxW9jke6jbsva3N5bMM_Q5zu6ak_qnCdjc0QG0UmcJ7wlTXIiLAQP5tw5qnj7hDoKQ9W_sxkRil32W11tM0p_50PtnUJRAhzNXppFmuxhWZJKA4_uxj6ulLogxMiR8uy_4YYMV56V_esFo6n-3lq=w640-h360" title="Operasi Campuran Pada Matriks" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 14. Operasi Campuran Pada Matriks</td></tr></tbody></table><br /><p style="text-align: justify;"><span style="font-size: medium;">Aplikasi Geogebra dari langkah-langkah diatas bisa dilihat dari link <a href="https://www.geogebra.org/m/pdarsnfw" rel="nofollow" target="_blank">https://www.geogebra.org/m/pdarsnfw</a></span></p><p style="text-align: justify;"><span style="font-size: medium;">Demikian pembahasan cara menggunakan aplikasi geogebra [ada matriks. Sebagai latihan kami persilahkan untuk melakukan operasi matriks dengan berbagai ordo yang berbeda. Selamat belajar dan semoga bermanfaat. Terimakasih.</span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-10674174918577360432022-10-01T10:26:00.002+08:002022-11-01T07:44:45.141+08:00Cara Menghitung Jarak Garis Ke Bidang Menggunakan Geogebra<p style="text-align: justify;"><span style="font-size: medium;"><b>Cara Menghitung Jarak Garis Ke Bidang Menggunakan Aplikasi Geogebra</b> - Pada pembahasan kali ini kita akan membahas cara menghitung jarak garis ke bidang menggunakan aplikasi geogebra. Tentunya dalam pembahasan ini akan membutuhkan penguasaan pada langkah-langkah penggunaan fitur-fitur aplikasi geogebra seperti yang sudah dijelaskan pada pembahasan-pembahasan sebelum ini.</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Cara menghitung jarak garis ke bidang menggunakan aplikasi geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Untuk lebih jelasnya cara menghitung jarak garis ke bidang menggunakan aplikasi geogebra pelajari contoh-contoh berikut</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Contoh</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sebuah Kubus ABCD.EFGH denngan panjang rusuk 8 cm. Hitunglah jarak garis AD ke bidang BCHE.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Penjelasan</b></span></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Gambarlah Kubus ABCD.EFGH dengan panjang rusuk 8 cm.</span></li><li><span style="font-size: medium;">Gambarlah Bidang BCHE</span></li><li><span style="font-size: medium;">Putarlah gambar yang sudah dibuat untuk mendapatkan view yang diinginkan</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZfGpbd151Z0ThVbHjb9SIN61L9fzgBMn53aeoBulxDFDLriNQonHU3LN2QZN2VGcmhVbYfP5WohOkDJpp7frUxYeFfeZjS-VhW495fqgr74F1M6xvpGCKHjsHbvM0vEe5AD-GNMc4MRBeuhxmqP8KBaWL_LO8J9X8Pj0W82T4zIf8s7hAhZetYTYn/s1366/geogebra%2019.png" style="margin-left: auto; margin-right: auto;"><img alt="Kubus dan bidang BCHE" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZfGpbd151Z0ThVbHjb9SIN61L9fzgBMn53aeoBulxDFDLriNQonHU3LN2QZN2VGcmhVbYfP5WohOkDJpp7frUxYeFfeZjS-VhW495fqgr74F1M6xvpGCKHjsHbvM0vEe5AD-GNMc4MRBeuhxmqP8KBaWL_LO8J9X8Pj0W82T4zIf8s7hAhZetYTYn/w640-h360/geogebra%2019.png" title="Kubus dan bidang BCHE" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Kubus dan Bidang BCHE</td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: justify;"><ul><li><span style="font-size: medium;">Buat sebuah bidang melalui AD dan berpotongan dengan bidang BCHE. Misal bidang ADFG</span></li><li><span style="font-size: medium;">Putar gambarnya untuk mendapatkan view yang tepat</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpCrt8YlbSL_9cAWOSArfcIPlvFKYmzHqktocr5RJ2fth5CEq73GtVwhLowfcgRMBRP3dWflYSzhr6EETP3Tc69sv-Js2yRAqqaGj7HUz1xa_puLrZXfk_IhG9bLyg0Cvy_Uc5AfpQHJmI8B6ajRdbflc9k-piOL8JSDVHWIYxjqm9Na_D1JJ9dSFO/s1366/geogebra%2020.png" style="margin-left: auto; margin-right: auto;"><img alt="Bidang ADGF berpotongan dengan bidang BCHE" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpCrt8YlbSL_9cAWOSArfcIPlvFKYmzHqktocr5RJ2fth5CEq73GtVwhLowfcgRMBRP3dWflYSzhr6EETP3Tc69sv-Js2yRAqqaGj7HUz1xa_puLrZXfk_IhG9bLyg0Cvy_Uc5AfpQHJmI8B6ajRdbflc9k-piOL8JSDVHWIYxjqm9Na_D1JJ9dSFO/w640-h360/geogebra%2020.png" title="Bidang ADGF berpotongan dengan bidang BCHE" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2 Bidang ADGF berpotongan dengan bidang BCHE</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><ul><li><span style="font-size: medium;">Untuk memperjelas garis-garis potong kedua bidang tersebut, klik Toolbar dengan gambar Kerucut yang dipotong bidang, kemudian klik garis AD dan bidang ADGF, lalu klik garis BC dan bidang BCHE.</span></li></ul></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpzzfqTac_QeSB6RA4NOW4SY89nlwAfOEndBpgworidVKeCvA_rSN_JFyaUIzvbgG5FOZ83MvnCj9Bq87mPaAtpHwBmNVBKNVpCuHSuGZiCg3fWBAUYJ0r_njWlmrGqDAsL7dTQG99oED0y4bQ1NlBUxzMYoRTlbpXwuyM1Y2jPPSarWc9Esv2oSFJ/s1366/geogebra%2021.png" style="margin-left: auto; margin-right: auto;"><img alt="Garis-garis potong bidang ADGF dan BCHE" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpzzfqTac_QeSB6RA4NOW4SY89nlwAfOEndBpgworidVKeCvA_rSN_JFyaUIzvbgG5FOZ83MvnCj9Bq87mPaAtpHwBmNVBKNVpCuHSuGZiCg3fWBAUYJ0r_njWlmrGqDAsL7dTQG99oED0y4bQ1NlBUxzMYoRTlbpXwuyM1Y2jPPSarWc9Esv2oSFJ/w640-h360/geogebra%2021.png" title="Garis-garis potong bidang ADGF dan BCHE" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Garis-garis potong bidang ADGF dan BCHE</td></tr></tbody></table><br /><p></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Sorot perpotongan kedua bidang ADGF dan BCHG, setelah muncul garis lalu klik, maka akan terbentuk garis n</span></li></ul><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6j7oErD4PfsMS-PbzR1kApYKHuONyUVg_6SbaNbO6BXalfAZSIvobnawRnc1s8s5gmU2Ut7QzonXr28rVVJiB8UELsmqxClutcPuuwimeoUcjr-3ZEtWQa9wNG62S2sHkodfun1J5FGl5GmH0gR7ogvfrGbRcYlFzB9yBtl1Jy74jCS-8QsPtRBw2/s1366/geogebra%2022.png" style="margin-left: auto; margin-right: auto;"><img alt="Garis potong bidang ADGF dan BCHE" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6j7oErD4PfsMS-PbzR1kApYKHuONyUVg_6SbaNbO6BXalfAZSIvobnawRnc1s8s5gmU2Ut7QzonXr28rVVJiB8UELsmqxClutcPuuwimeoUcjr-3ZEtWQa9wNG62S2sHkodfun1J5FGl5GmH0gR7ogvfrGbRcYlFzB9yBtl1Jy74jCS-8QsPtRBw2/w640-h360/geogebra%2022.png" title="Garis potong bidang ADGF dan BCHE" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Garis Potong Bidang ADGF dan BCHE</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Perhatikan bahwa garis AD sejajar dengan garis n dan proyeksi garis AD pada bidang BCHE adalah garis n, sehingga ambil salah satu titik pada garis AD misal titik A.h perpotongan garis AF dan BE misal titik Q.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Jarak garis AD ke bidang BCHE adalah panjang ruas garis AQ</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buka aplikasi CAS, hitung jarak titik A ke garis n. Ketik Jarak(J,Q). Perhatikan dari gambar tersebut pada titik A terbentuk juga titik J </span></li></ul><span style="text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK5kxCLSgj-GvDwpG3HyCiH9g7BUe_r4S5Uur2m4w8fFNPKGgL_lY4d5PLKGUFhmjKDoKzKMe1sVczMNbP_hjqXcqeIn-Rf-jFj6HxCwCTEPlPA4q1w2WIun8uRiRVk13etp02WO0iWsVki7doFE2x2GZACk0ynZLsjo-Q2vmcqfxyfvdHRCxOFzvk/s1366/geogebra%2023.png" style="margin-left: auto; margin-right: auto;"><img alt="Jarak garis AD ke bidang BCHE" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK5kxCLSgj-GvDwpG3HyCiH9g7BUe_r4S5Uur2m4w8fFNPKGgL_lY4d5PLKGUFhmjKDoKzKMe1sVczMNbP_hjqXcqeIn-Rf-jFj6HxCwCTEPlPA4q1w2WIun8uRiRVk13etp02WO0iWsVki7doFE2x2GZACk0ynZLsjo-Q2vmcqfxyfvdHRCxOFzvk/w640-h360/geogebra%2023.png" title="Jarak garis AD ke bidang BCHE" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Jarak garis AD ke bidang BCHE</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div></span><ul style="text-align: left;"><li><span style="font-family: inherit; font-size: medium;">Jadi jarak garis AD ke bidang BCHE adalah <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;4\sqrt{2}" style="text-align: justify;" title="4\sqrt{2}" /><span style="text-align: justify;"> cm</span></span></li></ul><br /></div><p style="text-align: justify;"><span style="font-size: medium;">Aplikasi geogebra untuk menghitung jarak garis ke bidang menggunakan geogebra diatas dapat dilihat melalui link berikut <a href="https://www.geogebra.org/m/sduww43s" rel="nofollow" target="_blank">https://www.geogebra.org/m/sduww43s</a></span></p><div style="text-align: justify;"><span style="font-size: medium;">Demikian pembahasan cara menghitung jarak garis ke bidang menggunakan geogebra, semoga bermanfaat dan terimakasih.</span></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-44443989030814496722022-09-14T21:11:00.002+08:002022-11-01T07:53:05.211+08:00Cara Menghitung Jarak Garis ke Garis Menggunakan Geogebra<p style="text-align: justify;"><span style="font-size: medium;"><b>Cara Menghitung jarak garis ke garis menggunakan aplikasi Geogebra -</b> Pada bahasan-bahasan sebelum ini sudah dibahas cara menghitung jarak garis ke garis secara perhitungan manual, baik melalui pendekatan geomteri maupun vektor, dan pada pembahasan kali ini akan dibahas cara menghitung jarak garis ke garis menggunakan aplikasi Geogebra.</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Cara Menghitung Jarak Garis ke Garis Menggunakan Geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Untuk lebih memahami cara menghitung jarak garis ke garis menggunakan Geogebra perhatikan langkah-langkahnya pada pembahasa soal-soal berikut.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Contoh 1</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Misalkan sebuah kubus ABCD.EFGH dengan panjang rusuk 10 cm, jika titik P adalah perpotongan diagonal bidang alas dan titik Q adalah perpotongan diagonal bidang tutup kubus tersebut. Hitunglah jarak garis AQ ke garis PG.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Bukalah aplikasi Geogebra Tampilan Grafik 3D.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Gambarlah kubus ABCD.EFGH dengan panjang rusuk 10 cm.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buat diagonal bidang alas kubus. Ketik <b><span style="color: red;">Ruasgaris(A,C),</span></b> diperoleh <b>garis f</b> dan <b><span style="color: red;">Ruasgaris(B,D)</span></b>, diperoleh <b>garis g</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Buat titik perpotongan kedua diagonal bidang alas tersebut. Ketik <b><span style="color: red;">Perpotongan(f,g)</span></b>, diperoleh <b>titik J</b>. Supaya sesuai dengan soal ganti nama <b>titik J </b>menjadi <b>titik P</b>.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buat diagonal bidang tutup kubus. Ketik <b><span style="color: red;">Ruasgaris(E,G)</span></b>, diperoleh <b>garis h</b> dan <b><span style="color: red;">Ruasgaris(F,H)</span></b>, diperoleh <b>garis i</b>.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buat titik perpotongan kedua diagonal bidang tutup tersebut. Ketik <b><span style="color: red;">Perpotongan(h,i)</span></b>, diperoleh <b>titik L</b>. Supaya sesuai dengan soal ganti nama<b> titik L</b> menjadi <b>titik Q</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Gambar Kubus ABCD.EFGH dari langkah-langkah diatas seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhRucRIhMclFeHwLJAAvCpAioNpJrXyrmhM7evNrUB8hmDPhfreQtSn1fIhUyHZ2RHbY32azTOk2oGn5Q_cmpzNfe_f204I2SbxozWxaHXUjigIxktXV4TC492IktSBz8rcIzVXGjnqWC5VqZNOHT1hij5uMW5ey-K95a8lU2YPYwmDORJ8Ythrj176" style="margin-left: auto; margin-right: auto;"><img alt="Kubus ABCD.EFGH dengan panjang rusuk 10" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhRucRIhMclFeHwLJAAvCpAioNpJrXyrmhM7evNrUB8hmDPhfreQtSn1fIhUyHZ2RHbY32azTOk2oGn5Q_cmpzNfe_f204I2SbxozWxaHXUjigIxktXV4TC492IktSBz8rcIzVXGjnqWC5VqZNOHT1hij5uMW5ey-K95a8lU2YPYwmDORJ8Ythrj176=w640-h360" title="Kubus ABCD.EFGH dengan panjang rusuk 10" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Kubus ABCD.EFGH Sesuai Dengan Soal Nomor 1</td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buatlah garis AQ. Ketik <b>Garis(A,Q)</b>, diperoleh <b>garis j</b>.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buatlah garis PG. Ketik <b>Garis(P,G)</b>, diperoleh <b>garis k</b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjsjhIukDB7ue2nCxOcZiflyrgLV44Vi5dp3ay13Avzsbr-YXRrHg0N0dPv2EnD7Lz0LgqhwkoUCV_rjxSqkn3or3zl5x46vlJAhaGhZU810zZLDEBjM1KdWZ4RPeaHMn7GjwTkRSt0wHxSk5MRkdpYphfdFdWkGSi8NekuiMoB3lv9SlA4WgY_fDA3" style="margin-left: auto; margin-right: auto;"><img alt="Garis AQ dan PG" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjsjhIukDB7ue2nCxOcZiflyrgLV44Vi5dp3ay13Avzsbr-YXRrHg0N0dPv2EnD7Lz0LgqhwkoUCV_rjxSqkn3or3zl5x46vlJAhaGhZU810zZLDEBjM1KdWZ4RPeaHMn7GjwTkRSt0wHxSk5MRkdpYphfdFdWkGSi8NekuiMoB3lv9SlA4WgY_fDA3=w640-h360" title="Garis AQ dan PG" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Garis AQ dan Garis PG</td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Pilih salah satu titik di garis AQ (garis j) atau garis PG (garis k). Misal pilih <b>titik Q</b> pada garis AQ (garis j). Proyeksikan titik Q pada garis PG (garis k), akan diperoleh <b>garis l</b>. Gunakan <b><span style="color: red;">Perpendicular Line</span></b>. Ingat pada langkah ini, karena garis j dan k sejajar maka untuk menentukan jarak kedua garis pilih salah satu titik yang ada di salah satu garis tersebut.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buat titik perpotongan garis l dan garis k. Ketik <b><span style="color: red;">Perpotongan(l,k)</span></b>, diperoleh <b>titik I</b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgksyORtkIWqeGUjHS8YuTpvZ4h3Ra_eZ6vMp_hLvk7f-1xZ0R7V56NuqTakXS-7KkupLofV_2zAiwtZZR7RCM5F8bxvnJzxzd1yAAkwmtuJFgFfZbfRPOlD-Z9tOve6f6pGGSSKMg51w4xTWuBpXGXmsSU5kFOAt6A5QUApBFXZsKC88ybLWslCeW1" style="margin-left: auto; margin-right: auto;"><img alt="Proyeksi Titik Q pada Garis PG" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgksyORtkIWqeGUjHS8YuTpvZ4h3Ra_eZ6vMp_hLvk7f-1xZ0R7V56NuqTakXS-7KkupLofV_2zAiwtZZR7RCM5F8bxvnJzxzd1yAAkwmtuJFgFfZbfRPOlD-Z9tOve6f6pGGSSKMg51w4xTWuBpXGXmsSU5kFOAt6A5QUApBFXZsKC88ybLWslCeW1=w640-h360" title="Proyeksi Titik Q pada Garis PG" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Proyeksi Titik Q pada Garis PG (garis k)</td></tr></tbody></table><br /><p></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Menghitung jarak titik Q ke titik I. Buka aplikasi <b>CAS.</b> Ketik J<b><span style="color: red;">arak(Q,I)</span></b></span></li></ul><p></p><p></p><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh3tDjNWSDbbixMMYfh2AZNLRX73ad0x8tJHBTykIxIk-7bkhO-KrWTyOq9uOKrVZow8bm_ik1ugUGDTXuxXmhFXa43CoVAeRAoui4ZXPgX2a0p7CdxZ0A_IXJDnTiOiFJo6er9ZRvYd76JrnJuyVhPRiylDxs92nJGU3JOM0fc02U20YpzpHDGQu90" style="margin-left: auto; margin-right: auto;"><img alt="Menghitung jarak titik Q ke titik I dengan CAS" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEh3tDjNWSDbbixMMYfh2AZNLRX73ad0x8tJHBTykIxIk-7bkhO-KrWTyOq9uOKrVZow8bm_ik1ugUGDTXuxXmhFXa43CoVAeRAoui4ZXPgX2a0p7CdxZ0A_IXJDnTiOiFJo6er9ZRvYd76JrnJuyVhPRiylDxs92nJGU3JOM0fc02U20YpzpHDGQu90=w640-h360" title="Menghitung jarak titik Q ke titik I dengan CAS" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Menghitung Jarak Titik Q Ke Titik I Dengan CAS</td></tr></tbody></table><br /><p></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;"><span>Jadi diperoleh jarak garis AQ ke garis PG adalah </span><img src="https://latex.codecogs.com/svg.image?\frac{10}{3}\sqrt{3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\frac{10}{3}\sqrt{3}" /> cm.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Aplikasi Geogebra dari penyelesaian soal diatas dapat dilihat melalui link <a href="https://www.geogebra.org/m/h9nwrzxh" rel="nofollow" target="_blank">https://www.geogebra.org/m/h9nwrzxh</a></span></li></ul><p></p><br /></div><p style="text-align: justify;"><span style="font-size: medium;"><b>Contoh 2</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui sebuah kubus ABCD.EFGH dengan panjang rusuk 2 cm Hitunglah j</span><span style="text-align: left;"><span style="font-size: medium;">arak garis BE ke garis DF.</span></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></span></p><p style="text-align: justify;"></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Buatlah Kubus ABCD.EFGH dengan panjang rusuk 2 cm</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buatlah garis BE. Ketik <span style="color: red;"><b>Garis(B,E)</b></span> akan diperoleh <b>garis f</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Buatlah garis DF. Ketik <b><span style="color: red;">Garis(D,F)</span></b>, akan diperoleh <b>garis g</b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgPA7dRAb18sm2VZlW6HsRmq2mbJTGadKmp4BopbXGzVvF_iwzMx6yfhahj-FbebcLnPOKDFdmXsoJHIJCZh_cbqjKNTArDFo51acHYNBxI-EpS83bNsgb7X-uINV3NHM2N0iuPpPLbRK8yxhtcrLkMLzksBGdckjlqXqCUoDWRQuc7acEHyemewfpY" style="margin-left: auto; margin-right: auto;"><img alt="Gambar Kubus ABCD.EFGH sesuai soal 2" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgPA7dRAb18sm2VZlW6HsRmq2mbJTGadKmp4BopbXGzVvF_iwzMx6yfhahj-FbebcLnPOKDFdmXsoJHIJCZh_cbqjKNTArDFo51acHYNBxI-EpS83bNsgb7X-uINV3NHM2N0iuPpPLbRK8yxhtcrLkMLzksBGdckjlqXqCUoDWRQuc7acEHyemewfpY=w640-h360" title="Gambar Kubus ABCD.EFGH sesuai soal 2" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Kubus ABCD.EFGH Sesuai Soal 2</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Buatlah garis sejajar dengan garis DF (garis g) dan melalui titik A. Klik Toolbar yang ada titik, garis dan bidang, kemudian Klik<b> Garis Sejajar.</b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiZqH_M2R92UVT8sPADgCJnkpF26m4EiiyLTisbEOdisIwRhDoZMFVji-QwYS5EFgKxQxSRm40JD-XPX4pF3JHs5lpC7mFmw2bnrz_JotX-rDSfiC-Vr66UcqXtdlwcAhB9M0OoS1wA5EbieEnwP5sC_0nZTXZumtjtOQvichJCKzN-mTbHJV0EWNep" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar garis sejajar" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiZqH_M2R92UVT8sPADgCJnkpF26m4EiiyLTisbEOdisIwRhDoZMFVji-QwYS5EFgKxQxSRm40JD-XPX4pF3JHs5lpC7mFmw2bnrz_JotX-rDSfiC-Vr66UcqXtdlwcAhB9M0OoS1wA5EbieEnwP5sC_0nZTXZumtjtOQvichJCKzN-mTbHJV0EWNep=w640-h360" title="Toolbar garis sejajar" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Toolbar garis sejajar</td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Klik <b>garis DF</b>, lalu klik <b>titik A</b>. diperoleh <b>garis h</b></span></li></ul><p></p><div><div class="separator" style="clear: both; text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzCZY6qQb7HF-xiYHks5fKmtJYYpxfJZW5PGRYfLu3QTan3TX6Q2INbaLj-SEfPIP_1QBvCmxBFhr2EG1AIprxdO8CxbispDcaZYoRyRsLLeieyMEIRnCcJpHif1HGOa4UUONQxONW08JJB6WY8JzsJSd05rNU3zL7L38T6_0m6S4ccLH-6RPM5rex/s1366/geogebra%2015.png" style="margin-left: auto; margin-right: auto;"><img alt="Garis sejajar DF melalui titik A" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzCZY6qQb7HF-xiYHks5fKmtJYYpxfJZW5PGRYfLu3QTan3TX6Q2INbaLj-SEfPIP_1QBvCmxBFhr2EG1AIprxdO8CxbispDcaZYoRyRsLLeieyMEIRnCcJpHif1HGOa4UUONQxONW08JJB6WY8JzsJSd05rNU3zL7L38T6_0m6S4ccLH-6RPM5rex/w640-h360/geogebra%2015.png" title="Garis sejajar DF melalui titik A" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Garis Sejajar DF Melalui Titik A</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div></div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buat bidang melalui garis g dan h. Ketik <b><span style="color: red;">Bidang(g,h)</span></b>, diperoleh <b>bidang p</b>.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Putar gambar sampai mendapat visual yang tepat untuk melihat titik potong bidang p dengan garis f, dengan cara klik panah kemudian drag gambar kubus.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio9LATiKsKLD2sovBAYivhqAc5R9hbtjUn-kUROZFmXhrn13BswbqyumcU3OrgKc6q4h3Xy1p9DSDHMzDmDYyDaPKpM753FxufuOZO0w1L3n9RcmIYgWwz5ViJyfv0PjBUZOsZ_SAN1HL3XnNd2WTummbQ21PyAdNgpvMyZ5RPuF7dRqZTxMRKyJm3/s1366/Geogebra%2016.png" style="margin-left: auto; margin-right: auto;"><img alt="Bidang p berpotongan dengan garis f" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio9LATiKsKLD2sovBAYivhqAc5R9hbtjUn-kUROZFmXhrn13BswbqyumcU3OrgKc6q4h3Xy1p9DSDHMzDmDYyDaPKpM753FxufuOZO0w1L3n9RcmIYgWwz5ViJyfv0PjBUZOsZ_SAN1HL3XnNd2WTummbQ21PyAdNgpvMyZ5RPuF7dRqZTxMRKyJm3/w640-h360/Geogebra%2016.png" title="Bidang p berpotongan dengan garis f" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Bidang p Berpotongan Dengan Garis f</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buat titik perpotongan garis f dengan bidang p. Ketik <b><span style="color: red;">Perpotongan(f,p)</span></b>, diperoleh <b>titik I</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Proyeksikan titik I ke garis DF (garis g). Gunakan <b>Perpendicular Line</b>, diperoleh <b>garis i.</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Tentukan titik perpotongan garis g dengan garis i. Ketik <b><span style="color: red;">Perpotongan(g,i)</span></b>, diperoleh <b>titik J</b></span></li></ul><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwrwdgOWNL8Kvt1eeRzWh8wcfGP1gtQz8k_v4P0p55wnoQiyv63urUNTgaWGQgLssCuNCtcEorUF3fqSkw9QXfxLU1KHjiSrOqwpcH_1WQY_fxXoVVQpG8ZUFbPozFIJ2SD-GbhkPZkxp9Yjb0ab0m-hcgSqFKnb2ftFZrPr_EdIX2vtAZtfGW6jz9/s1366/geogebra%2017.png" style="margin-left: auto; margin-right: auto;"><img alt="Proyeksi titik I ke garis g" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwrwdgOWNL8Kvt1eeRzWh8wcfGP1gtQz8k_v4P0p55wnoQiyv63urUNTgaWGQgLssCuNCtcEorUF3fqSkw9QXfxLU1KHjiSrOqwpcH_1WQY_fxXoVVQpG8ZUFbPozFIJ2SD-GbhkPZkxp9Yjb0ab0m-hcgSqFKnb2ftFZrPr_EdIX2vtAZtfGW6jz9/w640-h360/geogebra%2017.png" title="Proyeksi titik I ke garis g" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Proyeksi titik I ke garis g</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Menghitung jarak titik I ke titik J. Buka <b>CAS</b>, ketik <b><span style="color: red;">Jarak(I,J)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie69zF_LmnF9Uvk2AtqbJ1q3dGC5G7kp_yyh-eKcB_LlgFBI0kdrkmQC9cPQQw1Vi3qKwVzkQAuSefaQs940VAD4XOOmoLNX-2BMzoa71VTNdvdq_bnvVUC5iznkRJxzgKGjjw9mjZrRCP1tHIY5D5Az5QQBV5n89Th3QMmHLUL_vgWIDAqdAoj9EH/s1366/Geogebra%2018.png" style="margin-left: auto; margin-right: auto;"><img alt="Menghitung jarak titik I ke J dengan CAS" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie69zF_LmnF9Uvk2AtqbJ1q3dGC5G7kp_yyh-eKcB_LlgFBI0kdrkmQC9cPQQw1Vi3qKwVzkQAuSefaQs940VAD4XOOmoLNX-2BMzoa71VTNdvdq_bnvVUC5iznkRJxzgKGjjw9mjZrRCP1tHIY5D5Az5QQBV5n89Th3QMmHLUL_vgWIDAqdAoj9EH/w640-h360/Geogebra%2018.png" title="Menghitung jarak titik I ke J dengan CAS" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Menghitung Jarak Titik I ke Titik J dengan CAS</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Jadi jarak garis BE ke garis DF adalah <img src="https://latex.codecogs.com/svg.image?\frac{1}{3}\sqrt{6}" title="https://latex.codecogs.com/svg.image?\frac{1}{3}\sqrt{6}" /> cm.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Aplikasi Geogebra dari penyelesaian soal diatas dapat dilihat melalui link <a href="https://www.geogebra.org/m/fa25zy53" rel="nofollow" target="_blank">https://www.geogebra.org/m/fa25zy53</a></span></li><li style="text-align: justify;"><span style="font-size: medium;">Untuk melihat penyelesaian soal secara manual dapat dilihat melalui link <a href="https://www.sambimatika.my.id/2022/08/menghitung-jarak-garis-bersilangan-pada.html" rel="" target="_blank">https://www.sambimatika.my.id/2022/08/menghitung-jarak-garis-bersilangan-pada.html</a></span></li></ul><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Untuk soal-soal yang lainnya kami persilahkan untuk mencobanya secara mandiri. Demikian pembahasan cara menghitung jarak garis ke garis menggunakan aplikasi Geogebra, semoga bermanfaat.</span></p></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-81773192511618554552022-09-13T17:25:00.002+08:002022-11-01T07:56:02.127+08:00Cara Menghitung Jarak Titik Ke Bidang Menggunakan Geogebra<p style="text-align: justify;"><span style="font-size: medium;"><b>Cara Menghitung Jarak Titik Ke Bidang Menggunakan Geogebra -</b> Pada postingan sebelum ini sudah dibahas cara menghitung jarak titik ke garis pada bangun ruang, pada pembahasan kali ini akan dibahas cara menghitung jarak titik ke bidang menggunakan aplikasi geogebra.</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Cara Menghitung Jarak Titik Ke Bidang Menggunakan Geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Untuk lebih memahami cara menghitung jarak titik ke bidang menggunakan aplikasi geogebra pelajari contoh-contoh berikut.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Contoh 1</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui limas beraturan T.ABCD dengan panjang AB = 4 cm dan tinggi 4 cm. Hitunglah jarak titik B ke bidang TCD.</span></p><p style="text-align: justify;"><b style="font-size: large;">Pembahasan</b></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Buatlah Limas Beraturan T.ABCD dengan panjang rusuk alas 4 cm dan tinggi 4 cm.</span></li><li><span style="font-size: medium;">Buatlah bidang TCD. Ketik perintah <b><span style="color: red;">Bidang(T,C,D)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhAA_UsfpbyiAnPMgxaWKHIg_zc4LOiHpapT8ATOhcgCIbo1R1a34fbaaecl2AaJYSWKo7EQbVrXyPy8Ln7G7lccNUc23TbR50ugyyrnmcioa5kOLdSnA2euKVj-EiGvPbK-QZhzCek3mZ8IhmI51FhSiBVDjy3d-FZdKjxnXgUWoHXAcQDspzKVKR8" style="margin-left: auto; margin-right: auto;"><img alt="Bidang TCD pada limas" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhAA_UsfpbyiAnPMgxaWKHIg_zc4LOiHpapT8ATOhcgCIbo1R1a34fbaaecl2AaJYSWKo7EQbVrXyPy8Ln7G7lccNUc23TbR50ugyyrnmcioa5kOLdSnA2euKVj-EiGvPbK-QZhzCek3mZ8IhmI51FhSiBVDjy3d-FZdKjxnXgUWoHXAcQDspzKVKR8=w640-h360" title="Bidang TCD pada limas" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Bidang TCD Pada Limas</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Buat garis dari proyek titik B pada bidang TCD. Klik Toolbar yang ada garis titik dan bidang kemudian klik <b>Perpendicular Line</b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEio0Yya8pSEOC4wfAaVjOm-iNPlE0Ze7q7Pj_KXI_-KQkhoBk1tPq6O0eTPffLEl2YngFAd80jKw4TGiXMIVwLN9jU4ncuiBAmHyF_OiSjbpT12qxZRbu-OdwwxwyyWZSa4CeBXIxGx5-k1RbTG0SY364qqmous2JvZnlKSNxLHsYSFSsrhfC48Rn2D" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar Proyeksi" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEio0Yya8pSEOC4wfAaVjOm-iNPlE0Ze7q7Pj_KXI_-KQkhoBk1tPq6O0eTPffLEl2YngFAd80jKw4TGiXMIVwLN9jU4ncuiBAmHyF_OiSjbpT12qxZRbu-OdwwxwyyWZSa4CeBXIxGx5-k1RbTG0SY364qqmous2JvZnlKSNxLHsYSFSsrhfC48Rn2D=w640-h360" title="Toolbar Proyeksi" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Toolbar proyeksi</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Klik Titik B, selanjutnya klik bidang TCD pada area wana biru</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi2VflAFvfiXb816f0tnjb-g8bAnlNcp5gv1DcawdbkeHm3sHhKDmCCoInQnR-0lrgM98fJ2iPlJZlrUpsvEK3WjRb4L4MW-jfFFBmm3n3nw5quEFdazah1ywNuToJu8eoSJY5_JYO3bfx3yfz5OAOXEGMJVmPnrOLnxhvm8d7IDgoKLGLGI16k_0HE" style="margin-left: auto; margin-right: auto;"><img alt="Garis yang melalui titik B dan proyeksinya pada bidang TCD" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEi2VflAFvfiXb816f0tnjb-g8bAnlNcp5gv1DcawdbkeHm3sHhKDmCCoInQnR-0lrgM98fJ2iPlJZlrUpsvEK3WjRb4L4MW-jfFFBmm3n3nw5quEFdazah1ywNuToJu8eoSJY5_JYO3bfx3yfz5OAOXEGMJVmPnrOLnxhvm8d7IDgoKLGLGI16k_0HE=w640-h360" title="Garis yang melalui titik B dan proyeksinya pada bidang TCD" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Garis yang melalui titik B dan proyeksinya pada bidang TCD</td></tr></tbody></table><br /><p></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buat titik baru pada perpotongan garis f di bidang TCD, didapatkan garis E. Klik <b>toolbar yang ada titik dan huruf, kemudian klik Titik Baru</b>.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjjQb__xPYIQ4D5s6uJiSQBRzCJz0Gp93_jOWx4xGoHelrq0Onu9FvDlfJJVlyyAw8fVPhQ8fx_gVLGQjp0UEdZapp-6AsbzQoJxts6kOOJS4VWo09PiokUPdpe2bA_FxEFTRdkIa5Yp26TWKBuBSDvS9MwNXoxnkqe_l14FKcrMpio8eoCj0Zypidx" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar titik baru" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjjQb__xPYIQ4D5s6uJiSQBRzCJz0Gp93_jOWx4xGoHelrq0Onu9FvDlfJJVlyyAw8fVPhQ8fx_gVLGQjp0UEdZapp-6AsbzQoJxts6kOOJS4VWo09PiokUPdpe2bA_FxEFTRdkIa5Yp26TWKBuBSDvS9MwNXoxnkqe_l14FKcrMpio8eoCj0Zypidx=w640-h360" title="Toolbar titik baru" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Toolbar titik baru</td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Klik pada perpotongan garis dan bidang ditandai pada kurssor seperti gambar</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgr2OBhGVQ-v7GgIIWtcpTW9kSHWl921H5bkmOoVMCpgCGJakBjVsK137-g-ppALETrkcNrDaWmLrvRNXbZEgiRFoiF4zI5b_W048D5hm1vifP7OaVyvXE00SrGQARdbgBmydg0xoPPEa6KWj0qxnlRjPi30wS8EzpLd8QvOjsRKObzovKX6CBvnHhk" style="margin-left: auto; margin-right: auto;"><img alt="Tanda titik potong garis dan bidang" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgr2OBhGVQ-v7GgIIWtcpTW9kSHWl921H5bkmOoVMCpgCGJakBjVsK137-g-ppALETrkcNrDaWmLrvRNXbZEgiRFoiF4zI5b_W048D5hm1vifP7OaVyvXE00SrGQARdbgBmydg0xoPPEa6KWj0qxnlRjPi30wS8EzpLd8QvOjsRKObzovKX6CBvnHhk=w640-h360" title="Tanda titik potong garis dan bidang" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Tanda titik potong garis dan bidang</td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Hasil titik perpotongan garis f dengan bidang TCD seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj6QnFpoJNWDFMAFitgHsn5wrk0YdKC7L8yPHRNGfmipKOCt4G-XuFCduqjM15cCmxBrjSk4SThsdtYLq5wVlU-HKiR6vH0brDcsmrc-kD4hesoMy31H9LoSq1B1ka0RK_Ge5d5h08dKrBDOSFwFApaXGcLgludNeU-ggfKskdNrSZFrqswO7UrQ1Fa" style="margin-left: auto; margin-right: auto;"><img alt="Titik Perpotongan Garis f dan Bidang TCD" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEj6QnFpoJNWDFMAFitgHsn5wrk0YdKC7L8yPHRNGfmipKOCt4G-XuFCduqjM15cCmxBrjSk4SThsdtYLq5wVlU-HKiR6vH0brDcsmrc-kD4hesoMy31H9LoSq1B1ka0RK_Ge5d5h08dKrBDOSFwFApaXGcLgludNeU-ggfKskdNrSZFrqswO7UrQ1Fa=w640-h360" title="Titik Perpotongan Garis f dan Bidang TCD" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Titik Perpotongan Garis f dan Bidang TCD </td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buka aplikasi CAS kemudian ketik perintah <b><span style="color: red;">Jarak(B,E) </span></b>lalu tekan tombol Enter</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj_11jYo_NURPQwI_Gbw_F8t8VcojP7DU4_CUKyEnH_M-tJ0MayrRCLdXJAee7yqhAIP1bXtBX4TQgA61gGYTBcJeb9UekdIg_K5Qt_tbZeKvzJsgHPJi1PnPL3LFGOiioIPBYsflmEpZcOKo9IBfdfmOSv6qPulZWGKXJ4yKPAEdNKe-fMGmw1R4zc" style="margin-left: auto; margin-right: auto;"><img alt="Perhitungan jarak titik B ke bidang TCD dengan CAS" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEj_11jYo_NURPQwI_Gbw_F8t8VcojP7DU4_CUKyEnH_M-tJ0MayrRCLdXJAee7yqhAIP1bXtBX4TQgA61gGYTBcJeb9UekdIg_K5Qt_tbZeKvzJsgHPJi1PnPL3LFGOiioIPBYsflmEpZcOKo9IBfdfmOSv6qPulZWGKXJ4yKPAEdNKe-fMGmw1R4zc=w640-h360" title="Perhitungan jarak titik B ke bidang TCD dengan CAS" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Perhitungan jarak titik B ke bidang TCD dengan CAS</td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Jadi jarak titik B ke bidang TCD adalah <img src="https://latex.codecogs.com/gif.latex?\frac{8}{5}\sqrt{5}" title="\frac{8}{5}\sqrt{5}" /> cm.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Untuk melihat aplikasi Geogebra dari langkah penyelesaian diatas dapat dilihat melalui link <a href="https://www.geogebra.org/m/gugkmwjm" rel="nofollow" target="_blank">https://www.geogebra.org/m/gugkmwjm</a></span></li><li style="text-align: justify;"><span style="font-size: medium;">Pembahasan soal diatas secara manual dapat dilihat pada <a href="https://www.sambimatika.my.id/2020/08/pembahasan-soal-jarak-titik-ke-bidang.html" rel="" target="_blank">https://www.sambimatika.my.id/2020/08/pembahasan-soal-jarak-titik-ke-bidang.html</a></span></li></ul><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p></p><p></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Soal 2</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui kubus ABCD.EFGH dengan panjang rusuk 6 cm. Hitunglah jarak titik E ke bidang BDG.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Gambar kubus ABCD.EFGH dengan panjang rusuk 6 cm</span></li><li><span style="font-size: medium;">Buatlah bidang BDG dengan perintah <b><span style="color: red;">Bidang(B,D,G)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiTu4V1y54hz171FT0w8dlAbe9cctCTwAw0uHNSXbyqjEq7eBZQM86gHLr60tKHuk5jjT_Diu01S-VnGie9BbytzggQkzYIHxzRUzZGpR-m3bK5uEWIeT6pfsk8jczZLzpp8TojcxXQMewQlZAo0SS34hInRcKXRG5mVuK0oNG-rvP1YncQ7fcWPe63" style="margin-left: auto; margin-right: auto;"><img alt="Bidang BDG pada Kubus ABCD.EFGH" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiTu4V1y54hz171FT0w8dlAbe9cctCTwAw0uHNSXbyqjEq7eBZQM86gHLr60tKHuk5jjT_Diu01S-VnGie9BbytzggQkzYIHxzRUzZGpR-m3bK5uEWIeT6pfsk8jczZLzpp8TojcxXQMewQlZAo0SS34hInRcKXRG5mVuK0oNG-rvP1YncQ7fcWPe63=w640-h360" title="Bidang BDG pada Kubus ABCD.EFGH" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Bidang BDG (p) pada Kubus ABCD.EFGH</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Buat Garis yang melalui proyeksi titik E pada bidang BDG. Gunakan toolbar <b>Perpendicular Line</b>. Diperoleh garis f</span></li><li><span style="font-size: medium;">Buat titik perpotongan garis f dengan bidang BDG (p). Ketik perintah <span style="color: red; font-weight: bold;">Perpotongan(f,p) </span><span>diperoleh titik J</span></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi7Qy2CJIq38uap0eFd0BlqSCykb0didSK634FXg6NviTH_0Wfvcw4L_NopWgt3xjvRX3J8u6DzRDLVMDfItTyFFWRJiZlUNCTJIuvOPHgxnifkRXhbCFn9Ijf-mb3p9x9057VZR-qOXpryZFIAZoJQUHZLa8TZDFMMewC6lX-9kwRWmmcmJFusBcqe" style="margin-left: auto; margin-right: auto;"><img alt="Garis yang melalui titik E dan proyeksinya di bidang TCD" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEi7Qy2CJIq38uap0eFd0BlqSCykb0didSK634FXg6NviTH_0Wfvcw4L_NopWgt3xjvRX3J8u6DzRDLVMDfItTyFFWRJiZlUNCTJIuvOPHgxnifkRXhbCFn9Ijf-mb3p9x9057VZR-qOXpryZFIAZoJQUHZLa8TZDFMMewC6lX-9kwRWmmcmJFusBcqe=w640-h360" title="Garis yang melalui titik E dan proyeksinya di bidang TCD" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Garis yang melalui titik E dan proyeksinya di bidang TCD</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Buka <b>aplikasi CAS </b>dan hitunglah jarak titik E ke titik J. Ketik perintah <b><span style="color: red;">jarak(E,J)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEitPC78SH4hyd4Y28lLyAoRxqbXDTWcw5fGlM4wF8Uk6sc7CSDRLnHuHpPUdRk5UgGHjyM7ZKfymJ_jZDsJqD4xKfXJNGR5c2iY0H4yRichhRtRzFoCccNNO7mHrnXKxuVSXQLiE1CLD0xAltz33vPUGuT9yohvD5Ji4ESOnS_CPnhjKpDAhQA33Cd4" style="margin-left: auto; margin-right: auto;"><img alt="Perhitungan jarak titik E ke J dengan CAS" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEitPC78SH4hyd4Y28lLyAoRxqbXDTWcw5fGlM4wF8Uk6sc7CSDRLnHuHpPUdRk5UgGHjyM7ZKfymJ_jZDsJqD4xKfXJNGR5c2iY0H4yRichhRtRzFoCccNNO7mHrnXKxuVSXQLiE1CLD0xAltz33vPUGuT9yohvD5Ji4ESOnS_CPnhjKpDAhQA33Cd4=w640-h360" title="Perhitungan jarak titik E ke J dengan CAS" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Perhitungan jarak titik E ke J dengan CAS</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Jadi diperoleh jarak titik E ke bidang BDG adalah <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;4\sqrt{3}" style="text-align: left;" title="4\sqrt{3}" /><span style="text-align: left;"> </span><span style="font-family: inherit; text-align: left;">cm.</span></span></li><li style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: inherit; text-align: left;">Untuk melihat aplikasi Geogebra dari langkah penyelesaian diatas dapat dilihat melalui link <a href="https://www.geogebra.org/m/erxwenqa" rel="nofollow" target="_blank">https://www.geogebra.org/m/erxwenqa</a></span></span></li><li style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: inherit; text-align: left;">Untuk melihat pembahasan soal diatas secara manual dapat dilihat di <a href="https://www.sambimatika.my.id/2021/07/pembahasan-soal-jarak-titik-ke-bidang.html" rel="" target="_blank">https://www.sambimatika.my.id/2021/07/pembahasan-soal-jarak-titik-ke-bidang.html</a></span></span></li></ul><br /><p></p><p style="text-align: justify;"><span style="font-size: medium;">Demikian pembahasan cara menghitung jarak titik ke bidang menggunakan aplikasi Geogebra. Semoga bermanfaat.</span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-83809578849868928122022-09-12T19:28:00.003+08:002022-11-01T07:59:13.884+08:00Cara Menghitung Jarak Titik Ke Garis Menggunakan Geogebra<p style="text-align: justify;"><span style="font-size: medium;"><b>Cara Menghitung Jarak Titik Ke Garis Menggunakan Aplikasi Geogebra - </b> Pada postingan sebelum ini sudah dibahas cara menghitung jarak titik ke titik pada bangun ruang menggunakan aplikasi geogebra, kali ini akan dibahas cara mengitung jarak titik ke garis menggunakan aplikasi Geogebra</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Cara Menghitung Jarak Titik Ke Garis Menggunakan Geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Untuk memahami lebih jaruh cara menghitung jarak titik ke garis pada bangun ruang menggunakan aplikasi geogebra pelajarilah beberapa contoh berikut.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Contoh 1</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sebuah limas segi empat beraturan T.ABCD dengan panjang rusuk alas 3 cm dan tinggi limas 6 cm. Hitunglah jarak titik A ke rusuk TC</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Gambarlah limas segi empat beraturan T.ABCD diatas</span></li></ul><p></p><div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjp2UO9ZX-smaziJvgjtpsgDbxCJ7KVKhYXL29EmkKCx9WkA3SAukEmZr63zlbxfC3_bU5m8jnT18YgQEKZPHnnc7wWJ9-dfB4SdTyDa3MZpwdoMheDmRQf3nj_8vcV349mPueNx6KhsAalBdil_3WWxUnTMID1YUyVqFOflYaaSXinx_Bz857C-VXJ" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Gambar Limas T.ABCD" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjp2UO9ZX-smaziJvgjtpsgDbxCJ7KVKhYXL29EmkKCx9WkA3SAukEmZr63zlbxfC3_bU5m8jnT18YgQEKZPHnnc7wWJ9-dfB4SdTyDa3MZpwdoMheDmRQf3nj_8vcV349mPueNx6KhsAalBdil_3WWxUnTMID1YUyVqFOflYaaSXinx_Bz857C-VXJ=w640-h360" title="Gambar Limas T.ABCD" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Limas beraturan T.ABCD dengan panjang rusuk alas 3 cm dan tinggi 6 cm</td></tr></tbody></table><span style="font-size: medium;"><br /><br /></span></div><ul><li style="text-align: justify;"><span style="font-size: medium;">Tentukan proyeksi titik A pada garis TC. Klik toolbar yang ada titik, garis yang menembus bidang, kemudian klik Perpendicular Line.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjiKLy9ziYIh1gEPm9ym2PckCx_bdK5r99-1BZNtQBoNOfVXDQGiAOs2PH7FEbmbL5eIpGbA87z3gHunHEi71EjKupBuvmrmruuPBr_u-4mYY68xxo5kLpw_IfgPh4wcDVIXzvAPdESj39i0FppBDfepcL7MXy1jf0zflvTOFFY2nc8eijtgXOBtQPC" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Menentukan Proyeksi Titik Pada Garis" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjiKLy9ziYIh1gEPm9ym2PckCx_bdK5r99-1BZNtQBoNOfVXDQGiAOs2PH7FEbmbL5eIpGbA87z3gHunHEi71EjKupBuvmrmruuPBr_u-4mYY68xxo5kLpw_IfgPh4wcDVIXzvAPdESj39i0FppBDfepcL7MXy1jf0zflvTOFFY2nc8eijtgXOBtQPC=w640-h360" title="Menentukan Proyeksi Titik Pada Garis" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Toolbar menentukan proyeksi titik A pada garis TC</td></tr></tbody></table><span style="font-size: medium;"><br /></span><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Klik titik A, kemudian klik garis TC. Akan terbentuk garis yang melalui A dan tegak lurus garis TC</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgQHnRHslRIxrAFBEZKI2HzTyruzFDFaFPRCEdo7wtAYh3w5yeE7o72tJkn5eIl0PcHP4_GIi_Ra476dprhGjs0juQVy67tSLhYp9F-m8mlznT22awMotiWRQclt2RD3i8cN7bWXBCIeB2wz27JfUp4c1Vz8pl_5rv4ihyuU3Mx6QGzrr3PbSJnAbh2" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Proyeksi titik A ke garis TC" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgQHnRHslRIxrAFBEZKI2HzTyruzFDFaFPRCEdo7wtAYh3w5yeE7o72tJkn5eIl0PcHP4_GIi_Ra476dprhGjs0juQVy67tSLhYp9F-m8mlznT22awMotiWRQclt2RD3i8cN7bWXBCIeB2wz27JfUp4c1Vz8pl_5rv4ihyuU3Mx6QGzrr3PbSJnAbh2=w640-h360" title="Proyeksi titik A ke garis TC" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Garis yang melalui titik A ke proyeksinya pada garis TC dan tegak lurus TC</td></tr></tbody></table><span style="font-size: medium;"><br /></span><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buatlah titik baru yaitu perpotongan garis melalui titik A dan garis TC. Misalnya titik E. Klik <b>toolbar titik dan huruf</b>, kemudian klik <b>Titik Baru</b></span></li></ul><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj2Jj3mfN5p0KwjaSGomBmG7N6-VfSJ06PMurj9smqdjrHh5sJtrwYyvk44z3gG2yW6cnKPtf-hj5xvEq1VowXLK1JdM9d8hmYQ9FBJQg1H-kTaXzq9rwUeVZ3VIyPcheiVwwq4IklFyyDB0MBd2ytSWP5TFt2vSTowmWYPvv1b5HezfMpuXbj0R2WA" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar membuat titik baru" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEj2Jj3mfN5p0KwjaSGomBmG7N6-VfSJ06PMurj9smqdjrHh5sJtrwYyvk44z3gG2yW6cnKPtf-hj5xvEq1VowXLK1JdM9d8hmYQ9FBJQg1H-kTaXzq9rwUeVZ3VIyPcheiVwwq4IklFyyDB0MBd2ytSWP5TFt2vSTowmWYPvv1b5HezfMpuXbj0R2WA=w640-h360" title="Toolbar membuat titik baru" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Toolbar Membuat Titik Baru</td></tr></tbody></table><br /></span></div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Klik titik perpotongan garis melalui A dan TC</span></li></ul><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgEAAc0A9OJ3O9SMSQVd7TfI-4f3pxDQQ90PNeO2fI3_sABX6R5ia9WdWqYyE5iAtPO-tWzkpy7t5ycCuM7D9b850n7OZ-wqDQdFYdX87zTIW7IOssjlsnZ2LgwtdF6XTimaJYl3H9VxaPnJKhotyi8IZ2iGDhqyUFdGfh5EdtZTsEYh8TbuCudohno" style="margin-left: auto; margin-right: auto;"><img alt="Titik Potong Dua Garis" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgEAAc0A9OJ3O9SMSQVd7TfI-4f3pxDQQ90PNeO2fI3_sABX6R5ia9WdWqYyE5iAtPO-tWzkpy7t5ycCuM7D9b850n7OZ-wqDQdFYdX87zTIW7IOssjlsnZ2LgwtdF6XTimaJYl3H9VxaPnJKhotyi8IZ2iGDhqyUFdGfh5EdtZTsEYh8TbuCudohno=w640-h360" title="Titik Potong Dua Garis" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Titik E, perpotongan garis melalui A dan TC</td></tr></tbody></table><br /><br /></span></div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Tampilkan CAS</span></li><li style="text-align: justify;"><span style="font-size: medium;">Pada kotak Masukkan CAS ketik <b><span style="color: red;">Jarak(A,E)</span></b></span></li></ul><span style="font-size: medium;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgeFfi0NvdsxG99G8BRBP8YMe4ftcp1aknMLPFyDuaAsOTnS8EPNgdrYxebs4O1ny0k2JQDp3y6OcsqDjzUkLETP0I1TBQ0pSLN8nhniUZoa1GRuB82AY02n_SnWqglwubUADuKLjP1UhxhMZNooHOyrizUTAmCSUxheORhfwEn3_5CVRYB8wbhyTg2" style="margin-left: auto; margin-right: auto;"><img alt="Perhitungan Jarak Titik dan Garis Dengan CAS" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgeFfi0NvdsxG99G8BRBP8YMe4ftcp1aknMLPFyDuaAsOTnS8EPNgdrYxebs4O1ny0k2JQDp3y6OcsqDjzUkLETP0I1TBQ0pSLN8nhniUZoa1GRuB82AY02n_SnWqglwubUADuKLjP1UhxhMZNooHOyrizUTAmCSUxheORhfwEn3_5CVRYB8wbhyTg2=w640-h360" title="Perhitungan Jarak Titik dan Garis Dengan CAS" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Perhitungan Jarak Titik A ke Garis TC Dengan CAS</td></tr></tbody></table><br /><br /></span><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Maka jarak titik A ke garis TC adalah 4 cm</span></li><li style="text-align: justify;"><span style="font-size: medium;">Untuk melihat aplikasi Geogebra dari penyelesaian soal diatas dapat dilihat melalui link <a href="https://www.geogebra.org/m/umtvnftz" rel="nofollow" target="_blank">https://www.geogebra.org/m/umtvnftz</a></span></li></ul><p style="text-align: justify;"><span style="font-size: medium;">Sebagai referensi perhitugan manual dapat dilihat pada <a href="https://www.sambimatika.my.id/2021/07/soal-dan-pembahasan-jarak-titik-ke.html" rel="" target="_blank">Pembahasan Soal Jarak Titik Ke Garis Pada Bangun Ruang</a></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><table border="1" cellpadding="0" cellspacing="0" class="MsoTable15List6ColorfulAccent5" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid #4BACC6 .5pt; mso-border-bottom-themecolor: accent5; mso-border-top-alt: solid #4BACC6 .5pt; mso-border-top-themecolor: accent5; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr><td style="border-bottom: 1.5pt double windowtext; border-left: none; border-right: none; border-top: 1.5pt double windowtext; padding: 0cm 5.4pt; width: 478.8pt;" valign="top" width="638"><p class="MsoNormal" style="line-height: normal; margin-top: 12pt; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;">Baca Juga :<o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-instalasi-aplikasi-geogebra.html" rel="" target="_blank">Langkah-langkah Install Aplikasi Geogebra</a><o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-praktis-membuat-kubus-di.html" rel="" target="_blank">Langkah Praktis Membuat Kubus di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-limas-di-geogebra.html" rel="" target="_blank">Cara Menggambar Limas di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-membuat-titik-dan-garis-di-geogebra.html" rel="" target="_blank">Cara Menggambar Titik dan Garis di Aplikasi Geogebra</a></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-balok-di-geogebra.html" rel="" target="_blank">Cara Menggambar Balok di Aplikasi Geogebra</a></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-prisma-di-geogebra.html" rel="" target="_blank"><span style="font-size: medium;">Cara Menggambar Prisma di Aplikasi Geogebra</span></a></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><a href="https://www.sambimatika.my.id/2022/09/cara-menghitung-jarak-titik-ke-titik-menggunakan-aplikasi-geogebra.html" rel="" target="_blank"><span style="font-size: medium;"><b>Cara Meghitung Jarak Titik Ke Titik Menggunakan Apalikasi Geogebra</b></span></a></p></td></tr></tbody></table><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="-webkit-text-stroke-width: 0px; font-size: medium;"><span style="font-size: medium;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></span></p><p style="font-size: medium; text-align: left;"></p><p style="-webkit-text-stroke-width: 0px; font-size: medium;"><span style="font-size: medium;"><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-5542439818139892"></script><span style="text-align: left;"></span><!--Iklan tengah vertikal--><span style="text-align: left;"></span><ins class="adsbygoogle" data-ad-client="ca-pub-5542439818139892" data-ad-format="auto" data-ad-slot="5932457106" data-full-width-responsive="true" style="display: block; text-align: left;"></ins><script>
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</script></span></p><p></p><p style="-webkit-text-stroke-width: 0px; color: black; font-family: "Times New Roman"; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span style="font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Contoh 2</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui Kubus ABCD.EFGH dengan panjang AB = 10 cm. Hitunglah jarak titik H ke garis DF.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Gambar kubus ABCD.EFGH dengan panjang rusuk 10 cm</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi1trdc_T1dqCGNdKKKniRjv_VUHMcwgZxEaTHxLUSLoCyAEPFtlDTGvR4DxMqVpV5rjNCvjzzHkjH-pJFYRZoQuoZTFCsFFj-taeq8LJQaCnG-NPEtBKJWlCiK0y2Hcv_n0oEEPiRrkgM2KZIVXlg1ByIsR8jIOssqmpGaO4skVd--bYO6G1wseAlp" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Kubus dengan panjang rusuk 10 cm" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEi1trdc_T1dqCGNdKKKniRjv_VUHMcwgZxEaTHxLUSLoCyAEPFtlDTGvR4DxMqVpV5rjNCvjzzHkjH-pJFYRZoQuoZTFCsFFj-taeq8LJQaCnG-NPEtBKJWlCiK0y2Hcv_n0oEEPiRrkgM2KZIVXlg1ByIsR8jIOssqmpGaO4skVd--bYO6G1wseAlp=w640-h360" title="Kubus dengan panjang rusuk 10 cm" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Kubus ABCD.EFGH dengan panjang rusuk 10 cm</td></tr></tbody></table><span style="font-size: medium;"><br /></span><ul><li><span style="font-size: medium;">Buat ruas garis DF. Ketik <b><span style="color: red;">Ruasgaris(D,F)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhrCFWqOxfQKZZoxzeWXnfXK9Tvqkwo9KdAyyMg9tkVqSffaWch2V8ZVkaMPZxbyvTxNRd2KnTa--PxEQ9N0nqg4kaKJBQVHeevsZpAtuIaCg-JeBEYiqVkaVZbvEztpdXqHn1rXNAGgrlY0O0yH0rmGGsgY0UKa1p9iH1uGIQzrD2nsbqR2kuW_fcy" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Ruas Garis DF" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhrCFWqOxfQKZZoxzeWXnfXK9Tvqkwo9KdAyyMg9tkVqSffaWch2V8ZVkaMPZxbyvTxNRd2KnTa--PxEQ9N0nqg4kaKJBQVHeevsZpAtuIaCg-JeBEYiqVkaVZbvEztpdXqHn1rXNAGgrlY0O0yH0rmGGsgY0UKa1p9iH1uGIQzrD2nsbqR2kuW_fcy=w640-h360" title="Ruas Garis DF" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Ruas Garis DF</td></tr></tbody></table><span style="font-size: medium;"><br /></span><ul><li style="text-align: justify;"><span style="font-size: medium;">Buat Proyeksi titik H, ke garis DF. Klik toolbar yang ada titik, garis yang menembus bidang, kemudian klik <b>Perpendicular Line</b>. Kemudian Klik <b>titik H </b>dilanjutkan dengan Klik <b>garis DF</b>.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgiayn26g2UQqcpWEFqCb7BEwRP9eTkiqnHkRi3bu_ryAg1pzx925MFRcubK-G_KLiF2anN8pfCf_ENMY7r_bW7iSfGYRVF04l6jg19PskR7eqRixuw6owrM3k9edojkVJFDdK29eEJnsmG2x0aFU5nu_5QB0KC_aI8Ba7RHXioBLrgY1NTsA6AaQoi" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Garis yang melalui titik H dan tegak lurus DF" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgiayn26g2UQqcpWEFqCb7BEwRP9eTkiqnHkRi3bu_ryAg1pzx925MFRcubK-G_KLiF2anN8pfCf_ENMY7r_bW7iSfGYRVF04l6jg19PskR7eqRixuw6owrM3k9edojkVJFDdK29eEJnsmG2x0aFU5nu_5QB0KC_aI8Ba7RHXioBLrgY1NTsA6AaQoi=w640-h360" title="Garis yang melalui titik H dan tegak lurus DF" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Garis yang melalui titik H dan tegak lurus DF</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Buat Titik Baru yaitu perpotongan garis f dan g yaitu titik I</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEifcipeyHyFewtTCZI_x5l82AksyG4e60TAQL1MS4hb0Wr86LESFr4TIWif_J7-RTDTbFGWexvI8qaa2o-snYVkac4rJrjLZ22k02ZHytxqJlMKNhSX4aZZ-gGRRQmD62wJ5c4czwoNvrrMG6zM7IkXbf0Tz0oRGp6jkNGgcmfJMRvP5Y5c2v16uah5" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Titik Perpotongan garis f dan g" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEifcipeyHyFewtTCZI_x5l82AksyG4e60TAQL1MS4hb0Wr86LESFr4TIWif_J7-RTDTbFGWexvI8qaa2o-snYVkac4rJrjLZ22k02ZHytxqJlMKNhSX4aZZ-gGRRQmD62wJ5c4czwoNvrrMG6zM7IkXbf0Tz0oRGp6jkNGgcmfJMRvP5Y5c2v16uah5=w640-h360" title="Titik Perpotongan garis f dan g" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Titik Perpotongan garis f dan g</td></tr></tbody></table><span style="font-size: medium;"><br /></span><p></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Buka aplikasi CAS, lalu ketik <b><span style="color: red;">Jarak(H,I)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiwJpjZUEZti82lZM5yXR-8wKHZoFxqLphcAOaTP6FOdWm-JBOPy0gRXcWMvBmWiIMH0daqIJ1QN1I4INHLPHPtZ0MZDGg4p3XABypIWxE6QVZdGcXyAr4zIjJozk9hOpjqUyQdjq0cfGO0WH_sEtBQz724IlrxUR_-PVITc4O0fZEdnwRLLiGoSenJ" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Perhitungan jarak titik H ke I dengan CAS" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiwJpjZUEZti82lZM5yXR-8wKHZoFxqLphcAOaTP6FOdWm-JBOPy0gRXcWMvBmWiIMH0daqIJ1QN1I4INHLPHPtZ0MZDGg4p3XABypIWxE6QVZdGcXyAr4zIjJozk9hOpjqUyQdjq0cfGO0WH_sEtBQz724IlrxUR_-PVITc4O0fZEdnwRLLiGoSenJ=w640-h360" title="Perhitungan jarak titik H ke I dengan CAS" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 11. Perhitungan jarak titik H ke I dengan CAS</td></tr></tbody></table><span style="font-size: medium;"><br /></span><ul><li style="text-align: justify;"><span style="font-size: medium;">Jadi jarak titik H ke garis DF adalah <a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{10}{3}\sqrt{6}" style="font-family: verdana;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{10}{3}\sqrt{6}" title="\frac{10}{3}\sqrt{6}" /></a> cm.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Untuk melihat aplikasi Geogebra dari penyelesaian soal diatas dapat dilihat melalui link <a href="https://www.geogebra.org/m/hqjkayrq" rel="nofollow" target="_blank">https://www.geogebra.org/m/hqjkayrq</a></span></li></ul><span style="font-size: medium;"><div style="text-align: justify;">Untuk melihat hasi perhitungan manual bisa dilihat pembahasan soal nomor 3 pada <a href="https://www.sambimatika.my.id/2021/07/soal-dan-pembahasan-jarak-titik-ke.html" rel="" target="_blank">Pembahasan Soal Jarak Titik Ke Garis Pada Bangun Ruang</a></div></span><p></p><p><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Demikian pembahasan cara menghitung jarak titik ke garis menggunakan aplikasi Geogebra, semoga tulisan ini bermanfaat. Terimakasih</span></p><p></p><p></p></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-49390318190673137072022-09-11T16:51:00.003+08:002022-11-01T08:01:46.280+08:00Cara Menghitung Jarak Titik Ke Titik Menggunakan Geogebra<p style="text-align: justify;"><span style="font-size: medium;"><b>Cara Menghitung Jarak Titik Ke Titik Menggunakan Aplikasi Geogebra -</b> Dalam Pembelajaran Matematika di Kelas XII SMA/MA pokok bahasan Jarak Titik Pada Bangun Ruang, sering kali kita menggambarkan bangun ruang tidak dapat menujukkan garis yang merupakan jarak pada bangun ruang dengan jelas. Hal ini disebabkan karena untuk mendapatkan visual yang jelas ada kemungkinan gambar tersebut harus diputar sampai mendapatkan visual yang jelas. Ini menjadi kendala dan tantangan jika kita menggambar secara manual dan tanpa mempertimbangkan visualnya, yang pada ujungnya kita akan kesulitan menghitung jarak yang diinginkan.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Dengan aplikasi Geogebra diharapkan bisa menjadi kroscek pekerjaan menghitung jarak pada bangun ruang, baik dari segi gambar maupun hasil akhir perhitung. Baiklah kita akan bahas satu persatu dari kasus menghitung jarak pada bangun ruang ini. Pertama-tama kita akan mulai dengan cara menghitung jarak titik ke titik pada bangun ruang menggunakan aplikasi geogebra.</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Cara Menghitung Jarak Titik Ke Titik Menggunakan Geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Untuk lebih memahami </span><span style="text-align: left;"><span style="font-size: medium;">Menghitung Jarak Titik Ke Titik Menggunakan Aplikasi Geogebra pelajarilah beberapa pembahasan contoh soal berikut.</span></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-size: medium;"><b>Contoh 1</b></span></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-size: medium;">Pada Balok ABCD.EFGH dengan ukuran 4 x 3 x 4. Hitunglah jarak titik A ke titik G.</span></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></span></p><p style="text-align: justify;"></p><ul><li style="text-align: left;"><span style="font-size: medium;">Gambarlah Balok dengan ukuran 4 x 3 x 4</span></li></ul><div class="separator" style="clear: both; text-align: center;"><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5cbj55683i2-DnFiS6xvL_dXyjZoZjkAANiNCz7i97jN7D4tX-_O_b4lUSaM1m4rFvSRoBsLqCVMKVrt11HBa0G3kXI1q9Vn0Bl6ExSlaR5JSwipuhYylLvFlKpDRhE7kNV-nzQPxdjNjQYjDabYLixBRIbggFEIOhA-bAGsTCuuoDR1dQpe1HMsy/s1366/Geogebra%206.png" style="margin-left: auto; margin-right: auto;"><img alt="Balok dengan ukuran 4x3x4" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5cbj55683i2-DnFiS6xvL_dXyjZoZjkAANiNCz7i97jN7D4tX-_O_b4lUSaM1m4rFvSRoBsLqCVMKVrt11HBa0G3kXI1q9Vn0Bl6ExSlaR5JSwipuhYylLvFlKpDRhE7kNV-nzQPxdjNjQYjDabYLixBRIbggFEIOhA-bAGsTCuuoDR1dQpe1HMsy/w640-h360/Geogebra%206.png" title="Balok dengan ukuran 4x3x4" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Balok dengan ukuran 4x3x4</td></tr></tbody></table><p></p><br /></div><ul><li><span style="font-size: medium;">Gambarlah ruas garis yang merupakan jarak titik A ke titik G. Pada kotak Masukkan ketik perintan <b><span style="color: red;">Ruasgaris(A,G)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiipzWFoDqeyyPpQrmTMoQDtWPpcSc3xmUsyLUGVYNl60_FsrU73gr2j10kXg2d4dglJNuvGqp-KRxZw-3OsyobB3-VtoankLbdFA8otwRNtfu9w4iC93hFBmU0uN7BLJhNQlst2G3Eg5fgCKV_GUUieiS0aL6SfsVKoe8LstSJYr9sODn1sYIjhoT2/s1366/Geogebra%207.png" style="margin-left: auto; margin-right: auto;"><img alt="Garis jarak titik A ke titik G" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiipzWFoDqeyyPpQrmTMoQDtWPpcSc3xmUsyLUGVYNl60_FsrU73gr2j10kXg2d4dglJNuvGqp-KRxZw-3OsyobB3-VtoankLbdFA8otwRNtfu9w4iC93hFBmU0uN7BLJhNQlst2G3Eg5fgCKV_GUUieiS0aL6SfsVKoe8LstSJYr9sODn1sYIjhoT2/w640-h360/Geogebra%207.png" title="Garis jarak titik A ke titik G" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Ruas Garis f Merupakan Jarak Titik A ke titik G</td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Buka aplikasi CAS. Klik ikon <b>Garis Tiga yang ada gambar Limas</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Klik <b>Titik Tiga</b></span></li><li style="text-align: justify;"><span style="font-size: medium;">Klik <b>CAS</b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhReFFB_Zi9-ZPUxG2W-QYXd2a9xqzrCPy0akw3nj8IiBsQ8S_mUOQ-sNsl3funxZN6brXVftua_PjQlsDfo_naVE4zTi6d3VRp5VMNfxqjRNUo8-SFFHkTHuQ_Zd-dfoNLXFZDwASd5d1936DX-y0IeCmFrmw6b0NyNujeLgqKBOVcqByN0fdIA6u1/s1366/Geogebra%208.png" style="margin-left: auto; margin-right: auto;"><img alt="Menampilkan Aplikasi CAS" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhReFFB_Zi9-ZPUxG2W-QYXd2a9xqzrCPy0akw3nj8IiBsQ8S_mUOQ-sNsl3funxZN6brXVftua_PjQlsDfo_naVE4zTi6d3VRp5VMNfxqjRNUo8-SFFHkTHuQ_Zd-dfoNLXFZDwASd5d1936DX-y0IeCmFrmw6b0NyNujeLgqKBOVcqByN0fdIA6u1/w640-h360/Geogebra%208.png" title="Menampilkan Aplikasi CAS" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Menampilkan Aplikasi CAS</td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><ul style="text-align: left;"><li><span style="font-size: medium;">Tampilan Kotak CAS</span></li></ul><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiclstWVsj0RWqCtPTaecZrEeuwcAJ0d7WfLRHcnYa6_IAhn37ARufLidd4Yrt8Cx-_nV5W1U8MkQsnaFglZHeBPObY1yX83gH4LplPJqOR-vyhcJ88g-HuUpnF8ebCrmtI1ms4_udv1V-YCxsDgClW2b9k9CtwgyJ4LApj6ZBeVMckVJJA_-IkiU4D/s1366/Geogebra%209.png" style="margin-left: auto; margin-right: auto;"><img alt="Tampilan Kotak Masukkan CAS" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiclstWVsj0RWqCtPTaecZrEeuwcAJ0d7WfLRHcnYa6_IAhn37ARufLidd4Yrt8Cx-_nV5W1U8MkQsnaFglZHeBPObY1yX83gH4LplPJqOR-vyhcJ88g-HuUpnF8ebCrmtI1ms4_udv1V-YCxsDgClW2b9k9CtwgyJ4LApj6ZBeVMckVJJA_-IkiU4D/w640-h360/Geogebra%209.png" title="Tampilan Kotak Masukkan CAS" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Tampilan Kotak Masukkan CAS</td></tr></tbody></table><br /><div><ul style="text-align: left;"><li><span style="font-size: medium;">Pada kotak Masukkan CAS ketik <b><span style="color: red;">Jarak(A,G) </span>lalu tekan tombol Enter</b></span></li></ul><br /></div><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7N2Z6bK9dE5U-htLorfRtVoBxqOCyqSGoMpFc6N9RDMX4_CTo89XC0jzVVbO9SvbvU0H7UYWPtGc8uyvb0T4K7tk3rGcHfIjaxh-lpr1pycocyq1d04hWsvNYb99EAJ09z2f_XzhnEAavCbEKFizIB_yKNf0cPP4fqhvJ6PRSAAksd5IJ5QNGVz2y/s1366/Geogebra%2010.png" style="margin-left: auto; margin-right: auto;"><img alt="Perhitungan Jarak Titik A ke Titik G" border="0" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7N2Z6bK9dE5U-htLorfRtVoBxqOCyqSGoMpFc6N9RDMX4_CTo89XC0jzVVbO9SvbvU0H7UYWPtGc8uyvb0T4K7tk3rGcHfIjaxh-lpr1pycocyq1d04hWsvNYb99EAJ09z2f_XzhnEAavCbEKFizIB_yKNf0cPP4fqhvJ6PRSAAksd5IJ5QNGVz2y/w640-h360/Geogebra%2010.png" title="Perhitungan Jarak Titik A ke Titik G" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Perhitungan Jarak Titik A ke Titik G</td></tr></tbody></table><p></p><br /><div><ul style="text-align: left;"><li><span style="font-size: medium;">Jadi jarak titik A ke titik G adalah <img src="https://latex.codecogs.com/svg.image?\sqrt{41}" title="https://latex.codecogs.com/svg.image?\sqrt{41}" /></span></li><li style="text-align: justify;"><span style="font-size: medium;">Untuk melihat aplikasi Geogebra dari perhitungan soal diatas dapat dilihat melalu link <a href="https://www.geogebra.org/m/bgtkdju4" rel="nofollow" target="_blank">https://www.geogebra.org/m/bgtkdju4</a> </span></li></ul></div><p style="text-align: left;"><span style="font-size: medium;"><b><br /></b></span></p><table border="1" cellpadding="0" cellspacing="0" class="MsoTable15List6ColorfulAccent5" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid #4BACC6 .5pt; mso-border-bottom-themecolor: accent5; mso-border-top-alt: solid #4BACC6 .5pt; mso-border-top-themecolor: accent5; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr><td style="border-bottom: 1.5pt double windowtext; border-left: none; border-right: none; border-top: 1.5pt double windowtext; padding: 0cm 5.4pt; width: 478.8pt;" valign="top" width="638"><p class="MsoNormal" style="line-height: normal; margin-top: 12pt; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;">Baca Juga :<o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-instalasi-aplikasi-geogebra.html" rel="" target="_blank">Langkah-langkah Install Aplikasi Geogebra</a><o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-praktis-membuat-kubus-di.html" rel="" target="_blank">Langkah Praktis Membuat Kubus di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-limas-di-geogebra.html" rel="" target="_blank">Cara Menggambar Limas di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-membuat-titik-dan-garis-di-geogebra.html" rel="" target="_blank">Cara Menggambar Titik dan Garis di Aplikasi Geogebra</a></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-balok-di-geogebra.html" rel="" target="_blank">Cara Menggambar Balok di Aplikasi Geogebra</a></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-prisma-di-geogebra.html" rel="" target="_blank"><span style="font-size: medium;">Cara Menggambar Prisma di Aplikasi Geogebra</span></a></b></p></td></tr></tbody></table><p><span style="font-size: medium;"></span></p><p style="-webkit-text-stroke-width: 0px; font-size: medium; text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p></p><p style="-webkit-text-stroke-width: 0px; color: black; font-family: "Times New Roman"; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: justify; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-5542439818139892"></script><span style="text-align: left;"></span><!--Iklan tengah vertikal--><span style="text-align: left;"></span><ins class="adsbygoogle" data-ad-client="ca-pub-5542439818139892" data-ad-format="auto" data-ad-slot="5932457106" data-full-width-responsive="true" style="display: block; text-align: left;"></ins><script>
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</script></p><p style="text-align: left;"><span style="font-size: medium;"><b>Contoh 2.</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui Kubus ABCD.EFGH dengan panjang rusuk 4 cm. Jika titik P terletak di pertengahan rusuk BC dan titik Q merupakan perpotongan garis EG dan HF. Hitunglah jarak titik P ke titik Q.</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"></p><ul><li><span style="font-size: medium;">Gambar Kubus ABCD.EFGH dengan panjang rusuk 4</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgFcja6i0HXkP-C4b6gPO6MOjAd4x0hqB3pP8tzby4i2ieu2npF16wpjGrlSD6oN1deaA0fdfUI4OJ-L05_aUByGNDvJlt67JqBdxCXL30AjwS_1fFmE9Nnsg_mTz9ySF6KXJ0loT0wnOdl4TmT7MABUtmovOUcEvXRjrFAC6mUgzPWxEF54LR_5UpB" style="margin-left: auto; margin-right: auto;"><img alt="Kubus ABCD.EFGH dengan panjang rusuk 4" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgFcja6i0HXkP-C4b6gPO6MOjAd4x0hqB3pP8tzby4i2ieu2npF16wpjGrlSD6oN1deaA0fdfUI4OJ-L05_aUByGNDvJlt67JqBdxCXL30AjwS_1fFmE9Nnsg_mTz9ySF6KXJ0loT0wnOdl4TmT7MABUtmovOUcEvXRjrFAC6mUgzPWxEF54LR_5UpB=w640-h360" title="Kubus ABCD.EFGH dengan panjang rusuk 4" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Kubus ABCD.EFGH dengan panjang rusuk 4</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Tentukan titik P di pertengahan rusuk BC. Pada kotak Masukkan ketik <b><span style="color: red;">Titiktengah(B,C)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiRBr3MvuK1baozk98btoEwYswFTTum0m__wysvA9IEuJpULZoc2D-aE55ErWNoG5HUAj7Dp8HHs_bcXvq_hfwnwOgPdJ7diOmkl7mk9amnqGFqWxBynNO30T3EPs9qX2Xwqe2nxj4hSW6n6l0zCmrIKpCVjfnsbmvlhb1APQDNq4YSLfDhdUOKsTm7" style="margin-left: auto; margin-right: auto;"><img alt="Titik Tengah Garis" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiRBr3MvuK1baozk98btoEwYswFTTum0m__wysvA9IEuJpULZoc2D-aE55ErWNoG5HUAj7Dp8HHs_bcXvq_hfwnwOgPdJ7diOmkl7mk9amnqGFqWxBynNO30T3EPs9qX2Xwqe2nxj4hSW6n6l0zCmrIKpCVjfnsbmvlhb1APQDNq4YSLfDhdUOKsTm7=w640-h360" title="Titik Tengah Garis" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Titik Tengah Garis BC</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Label titik tengah BC adalah titik I. Untuk menyesuaikan nama titik dengan soal, kita harus edit nama titik I. Klik <b>toolbar panah</b>. <b>Klik kanan titik I, klik Namai Ulang</b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgGXUAX3EVnW6m1Byuj4xFBXTLDgv9VmiNoS_haGXNspagqSFqImaQRbw2LIGfqNbY_93Y5gz3-0orKJhFW9UdoB2-pZPMNwZoVlM4SUHGBXSYVHtp3b4zE4weCOn_xvpPcdwWkkphefKAwKK-XZ7TLm3oFwRgYPFR4J-ZL9rY41zeL8gvt1nkzmDAJ" style="margin-left: auto; margin-right: auto;"><img alt="Menamai Ulang Titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgGXUAX3EVnW6m1Byuj4xFBXTLDgv9VmiNoS_haGXNspagqSFqImaQRbw2LIGfqNbY_93Y5gz3-0orKJhFW9UdoB2-pZPMNwZoVlM4SUHGBXSYVHtp3b4zE4weCOn_xvpPcdwWkkphefKAwKK-XZ7TLm3oFwRgYPFR4J-ZL9rY41zeL8gvt1nkzmDAJ=w640-h360" title="Menamai Ulang Titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Menamai Ulang Titik I</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Ubah I menjadi P, lalu klik tombol OK</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiaIvADCBElBz_N1VVpp8n4kd9itsjtUBMlyp8DswURxzMPQKcqMuqsAZZ_jgZJOS9NQgLm1lqOOZzoIr0MIDKN8FkcsPOAKv_v1hju00Ihyx2d25wQo1Ex6wPaNRHBl6v-QXyDGCbjinbxVJkemOjPvgu-Z9SmneRYn6Zw82IifKpOvtOfbNyEsnxp" style="margin-left: auto; margin-right: auto;"><img alt="Mengganti Nama Titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiaIvADCBElBz_N1VVpp8n4kd9itsjtUBMlyp8DswURxzMPQKcqMuqsAZZ_jgZJOS9NQgLm1lqOOZzoIr0MIDKN8FkcsPOAKv_v1hju00Ihyx2d25wQo1Ex6wPaNRHBl6v-QXyDGCbjinbxVJkemOjPvgu-Z9SmneRYn6Zw82IifKpOvtOfbNyEsnxp=w640-h360" title="Mengganti Nama Titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Mengganti Nama Titik I Menjadi Titik P</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Buatlah ruas garis EG dan FH. Pada kotak Masuukan ketik <b><span style="color: red;">ruasgaris(E,G)</span></b> lalu tekan Enter. Kemudian ketik <span style="color: red;"><b>ruasgaris(F,H)</b></span> lalu tekan Enter.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgFXqmWm9H1MmTybj3MnmoHGVuLbFi9sE7qBbGjnDt7J_dR2V8Irb_Z4-xsFppQYS0oQjVes8P-cHq2CBvaoDDyvj7pk8brRxK-UoGxoAme-TWZAfP9QtsCNSXI-UhyhBu5xy3eRSntV71ZX6rIy66iYmiOy4pEWpX9IJOON2TY48UxaeZexD22Wsmj" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Ruas Garis EG dan FH" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgFXqmWm9H1MmTybj3MnmoHGVuLbFi9sE7qBbGjnDt7J_dR2V8Irb_Z4-xsFppQYS0oQjVes8P-cHq2CBvaoDDyvj7pk8brRxK-UoGxoAme-TWZAfP9QtsCNSXI-UhyhBu5xy3eRSntV71ZX6rIy66iYmiOy4pEWpX9IJOON2TY48UxaeZexD22Wsmj=w640-h360" title="Membuat Ruas Garis EG dan FH" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Membuat Ruas Garis EG dan FH</td></tr></tbody></table><br /><p></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Buatlah titik perpotongan ruas garis EG dan FH. Ketik <b><span style="color: red;">perpotongan(f,g)</span></b>. f = nama ruas garis EG dan g nama ruas garis FH</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhHPfrtqqbBi9MMjhkmYoCjq08Svcx2A1T0O7vzgPELXnXuXHbA819xyZkxRF2p8kpKkyb2TleyM_mmCc7ymY59hmKiMp1N7JwHY0NBMYRiub0q5Djb1-nPrqSXqGo8dpO4chxup8hHFttoGeU_sTo_zNmQFRdiJJzuyAHEQmUfeYTyGY3CyBv7V6RK" style="margin-left: auto; margin-right: auto;"><img alt="Perpotongan garis EG dan FH" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhHPfrtqqbBi9MMjhkmYoCjq08Svcx2A1T0O7vzgPELXnXuXHbA819xyZkxRF2p8kpKkyb2TleyM_mmCc7ymY59hmKiMp1N7JwHY0NBMYRiub0q5Djb1-nPrqSXqGo8dpO4chxup8hHFttoGeU_sTo_zNmQFRdiJJzuyAHEQmUfeYTyGY3CyBv7V6RK=w640-h360" title="Perpotongan garis EG dan FH" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 11. Perpotongan ruas garis EG dan FH</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Ubah nama titik I menjadi titik Q</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiJSYrA20iFbn-4ZmmD55PlYrce2ConY8HTwpHxWoelxSkF8yIJvyjwlHDxK45YJTHh3F8VVOip-3mKnkedGo_UsuhYcWAIuOjTFKJj_Ao5u2jK6DgwJRPDPk8d-5kRrGgMfq4mBg67oXUtFDgJjIs6vA18IrTuvbgRRG0gkhi2O9GeAdtGGfzfgGJk" style="margin-left: auto; margin-right: auto;"><img alt="Menguban Nama Titik I menjadi Titik Q" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiJSYrA20iFbn-4ZmmD55PlYrce2ConY8HTwpHxWoelxSkF8yIJvyjwlHDxK45YJTHh3F8VVOip-3mKnkedGo_UsuhYcWAIuOjTFKJj_Ao5u2jK6DgwJRPDPk8d-5kRrGgMfq4mBg67oXUtFDgJjIs6vA18IrTuvbgRRG0gkhi2O9GeAdtGGfzfgGJk=w640-h360" title="Menguban Nama Titik I menjadi Titik Q" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 12. Menguban Nama Titik I menjadi Titik Q</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Buat ruas garis PQ, yang merupakan jarak titik P ke titik Q. Ketik <b><span style="color: red;">ruasgaris(P,Q)</span></b></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiGcBeY64toJcDpJRqx6Dnxqy0HqoAwLkpOPBJuOKDkZSJejvbFGXEWEfkcuhLBXbcbLvF2Kl6n3o4J_i4sSJuwj2mM42T2mR7dzNSJMr_7tXY6cWKtVxiK1hbrAiADrF7qidBGySEsgieQpHJMXv27xh8i7tNUZR8eDKH3sQs3O8MbIuFrbd4MEXiG" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Ruas Garis PQ" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiGcBeY64toJcDpJRqx6Dnxqy0HqoAwLkpOPBJuOKDkZSJejvbFGXEWEfkcuhLBXbcbLvF2Kl6n3o4J_i4sSJuwj2mM42T2mR7dzNSJMr_7tXY6cWKtVxiK1hbrAiADrF7qidBGySEsgieQpHJMXv27xh8i7tNUZR8eDKH3sQs3O8MbIuFrbd4MEXiG=w640-h360" title="Membuat Ruas Garis PQ" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 13. Ruas Garis PQ yang merupakan jarak titik P ke titik Q</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Menghitung jarak titik P ke titik Q. Buka aplikasi CAS, kemudian ketik <b><span style="color: red;">jarak(P,Q)</span></b> lalu tekan tombol Enter</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi4ReWYp55K76QVZo73pKTlYuEbLCG0TaIAR7NvwnymQoFBeKNne0UbIbPZJQoLPuVNo-ETl8QRq8bTen0fQeANEEM7qURui9OH3X7PdwMflkyKbGcGy0LUk8H73_qhhUBkOpdntJd3IVjfX2SSEd2DbwaDQA4qHYIZtEzj5nApQ6CVq2NLrhFFcNsO" style="margin-left: auto; margin-right: auto;"><img alt="Menghitung jarak titik P ke titik Q" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEi4ReWYp55K76QVZo73pKTlYuEbLCG0TaIAR7NvwnymQoFBeKNne0UbIbPZJQoLPuVNo-ETl8QRq8bTen0fQeANEEM7qURui9OH3X7PdwMflkyKbGcGy0LUk8H73_qhhUBkOpdntJd3IVjfX2SSEd2DbwaDQA4qHYIZtEzj5nApQ6CVq2NLrhFFcNsO=w640-h360" title="Menghitung jarak titik P ke titik Q" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 14. Menghitung jarak titik P ke titik Q</td></tr></tbody></table><br /><p></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Jadi diperoleh jarak titik P ke titik Q adalah <img src="https://latex.codecogs.com/svg.image?2\sqrt{5}" title="https://latex.codecogs.com/svg.image?2\sqrt{5}" /></span></li><li style="text-align: justify;"><span style="font-size: medium;">Untuk melihat aplikasi Geogebra dari perhitungan soal diatas dapat dilihat melalu link <a href="https://www.geogebra.org/m/rkxrue8q" rel="nofollow" target="_blank">https://www.geogebra.org/m/rkxrue8q</a></span></li></ul><div style="text-align: justify;"><span style="font-size: medium;"><br /></span></div><div style="text-align: justify;"><span style="font-size: medium;">Untuk penyelesaiannya kasus-kasus yang lain, silahkan anda buat soal sendiri dan gunakan langkah-langkah diatas sebagai referensi. Demikian pembahasan </span><span style="text-align: left;"><span style="font-size: medium;">Cara Menghitung Jarak Titik Ke Titik Menggunakan Aplikasi Geogebra, semoga bermanfaat.</span></span></div><p></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-89482566459156010302022-09-10T07:34:00.003+08:002022-11-01T08:03:41.402+08:00Cara Menggambar Prisma Di Geogebra<p style="text-align: justify;"><span style="font-size: medium;"><b></b></span></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP92PfVcf4g51axW5E9Qy9UZMMeMPismMgWwHyfspgBp8FnqE6R4ACSP94_iXci7F1QkSNpkXinzAvmFrPMl7fDXjDpqk89A-zTqoyqZ9aZr7M_DuNbOBEcP5BghYcfbzanQkVbYnR79yo0qzN44GCQt7wsgfwT-xEA2xjnfa41vLWfKC9qGinc2Q6/s754/geogebra%205.png" style="margin-left: 1em; margin-right: 1em;"><img alt="Prisma Segi-n beraturan" border="0" data-original-height="510" data-original-width="754" height="135" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP92PfVcf4g51axW5E9Qy9UZMMeMPismMgWwHyfspgBp8FnqE6R4ACSP94_iXci7F1QkSNpkXinzAvmFrPMl7fDXjDpqk89A-zTqoyqZ9aZr7M_DuNbOBEcP5BghYcfbzanQkVbYnR79yo0qzN44GCQt7wsgfwT-xEA2xjnfa41vLWfKC9qGinc2Q6/w200-h135/geogebra%205.png" style="float: left; margin: 5px 9px;" title="Prisma Segi-n beraturan" width="200" /></a></b></span></div></div><span style="font-size: medium;"><div style="text-align: justify;"><b>Cara Menggambar Prisma Di Geogebra - </b>Prisma adalah bangun ruang yang memiliki dua sisi sejajar dengan bentuk dan ukuran yang sama. Kalau menurut Kamus Besar Bahasa Indonesia (KBBI), prisma adalah bidang banyak yang memiliki sepasang sisi sejajar dan sebangun yang disebut alas dan sisi-sisi lain yang disebut tinggi.</div></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Menggambar Prisma di aplikasi Geogebra.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Menggambar Prisma di Geogebra caranya hampir mirip dengan menggambar bangun ruang lainnya seperti Kubus dan Balok. Format perintah menggambar Prisma dalam postingan ini menggunakan format "Prisma(Poligon alas,tinggi prisma).</span></p><p style="text-align: justify;"><span style="font-size: medium;">Yang perlu diperharikan adalah alas prisma dapat berbentuk Segitiga, Persegi, Persegi Panjang, Segi 5, Segi 6 atau mungkin yang lain. Dalam postingan ini akan dibahas beberapa bentuk dari prisma tersebut.</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Cara Menggambar Prisma Di Geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Langkah-langkah menggambar Prismma Segi-5 beraturan di Geogebra.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal kita akan menggambar Prisma Segi-5 Beraturan dengan panjang rusuk alas 4 cm dan tinggi prisma 3 cm</span></p><p style="text-align: justify;"></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Buka aplikasi Geogebra Classic 6 versi desktop atau versi online di <a href="https://geogebra.org/classic" rel="nofollow" target="_blank">https://geogebra.org/classic</a> dan pilih Tampilan Grafik 3D</span></li><li style="text-align: justify;"><span style="font-size: medium;">Gambarlah alas prisma berbentuk segi-6. Klik Toolbar Segitiga dan Klik Segi-n Beraturan.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjmJbmfsmPpT75Ut1b1T3wDdpnY8Js-fipT9puw0_fh3ad2_MV_q0KRew-PfMEJATvDldz8S4sSsys3meAAUMxp4o4OkTn6Xdy0R5BIKrXvcdL8WN3xl_3MPZImZdzMy0NEgW8qYcNIshIts4FJN0aVbxo1ORms4fUNmraKGSk7x7N_rc1DVUOUDJTn" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar Menggambar Segi-n Beraturan" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjmJbmfsmPpT75Ut1b1T3wDdpnY8Js-fipT9puw0_fh3ad2_MV_q0KRew-PfMEJATvDldz8S4sSsys3meAAUMxp4o4OkTn6Xdy0R5BIKrXvcdL8WN3xl_3MPZImZdzMy0NEgW8qYcNIshIts4FJN0aVbxo1ORms4fUNmraKGSk7x7N_rc1DVUOUDJTn=w640-h360" title="Toolbar Menggambar Segi-n Beraturan" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Toolbar Menggambar Segi-n Beraturan</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Pada bidang kartesius klik titik pertama misal (0,0,0) dan titik (4,0,0), kemudian akan muncul kotak isian untuk mengisi banyak segi yang akan dibuat. Karena kita akan membuat segi-5, masukkan 5</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiMsqgUZj7smXwThupbS5WM-Pqk1ezeFlfBVBpUefRaC3lKdncPhoMcTibf88HauyagSzcAbGyYFa1493koByxVseWE2GjMYfq5GxzaWMejOdUNWe4mR8so_HYrLy561z7-D4l_smMD6Wp4sEuFOi2Qibnz8IyX8ARRAuRri58rU9ZzECf2yEvwql3q" style="margin-left: auto; margin-right: auto;"><img alt="Kotak Isian Banyak Segi Alas Prisma" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiMsqgUZj7smXwThupbS5WM-Pqk1ezeFlfBVBpUefRaC3lKdncPhoMcTibf88HauyagSzcAbGyYFa1493koByxVseWE2GjMYfq5GxzaWMejOdUNWe4mR8so_HYrLy561z7-D4l_smMD6Wp4sEuFOi2Qibnz8IyX8ARRAuRri58rU9ZzECf2yEvwql3q=w640-h360" title="Kotak Isian Banyak Segi Alas Prisma" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Kotak Isian Banyak Segi Alas Prisma</td></tr></tbody></table><br /><ul><li style="text-align: justify;"><span style="font-size: medium;">Hasilnya akan tampak seperti gambar berikut</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhsckNnwF9j0SvJ4HQZkt1EYetJ4n2GEbTDozpqQqD5QjF8k_YpKf1Nu0lUzJtgh1mQM6G_z_Fnjai2fNOx9oG1ixUJKn7a9tHf3jpcRuUy1swbdKYgBouTIn13aMAHicXCtTM6QEuNkQ1XwUITiaVzDD_m8Fr_1VrEIhw9_LvwYq-xDsyQ7fUDENQ4" style="margin-left: auto; margin-right: auto;"><img alt="Segi-5 Beraturan" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhsckNnwF9j0SvJ4HQZkt1EYetJ4n2GEbTDozpqQqD5QjF8k_YpKf1Nu0lUzJtgh1mQM6G_z_Fnjai2fNOx9oG1ixUJKn7a9tHf3jpcRuUy1swbdKYgBouTIn13aMAHicXCtTM6QEuNkQ1XwUITiaVzDD_m8Fr_1VrEIhw9_LvwYq-xDsyQ7fUDENQ4=w640-h360" title="Segi-5 Beraturan" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Segi-5 Beraturan</td></tr></tbody></table><br /><ul><li><span style="font-size: medium;">Pada kotak Masukkan ketik perintah <b><span style="color: red;">Prisma(poli1,3)</span></b>. Keterangan : poli1 = nama segi-5 yang sudah dibuat (lihat di daftar pada bagian kotak masukkan). 3 = tinggi prisma</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjOGLN7Bxvrb6lg8vK78N00kC6nkZ__ABiX_QvPmuYpfUfNvJhh30cqORoMomy60rX9-ejCrqBCP9RzLj8XZ8IQ6QZv1F2A6RzHKUR8MH-EfVCuSxqEr7wkb3VFN6ONFetrcsJyAn2rzClK-hjmCuHm2brtCZp4W_NV6IPo3Z1Qxl7_Nbwf4YeF9JFP" style="margin-left: auto; margin-right: auto;"><img alt="Gambar Prisma Segi-5 Beraturan" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjOGLN7Bxvrb6lg8vK78N00kC6nkZ__ABiX_QvPmuYpfUfNvJhh30cqORoMomy60rX9-ejCrqBCP9RzLj8XZ8IQ6QZv1F2A6RzHKUR8MH-EfVCuSxqEr7wkb3VFN6ONFetrcsJyAn2rzClK-hjmCuHm2brtCZp4W_NV6IPo3Z1Qxl7_Nbwf4YeF9JFP=w640-h360" title="Gambar Prisma Segi-5 Beraturan" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Prisma Segi-5 beraturan ukuran rusuk alas 4 cm dan tinggi 3 cm</td></tr></tbody></table><br /><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-size: medium;">Aplikasi Geogebra dari gambar prisma diatas dapat dilihat melalui link berikut <a href="https://www.geogebra.org/m/eyhjpuzk" rel="nofollow" target="_blank">https://www.geogebra.org/m/eyhjpuzk</a></span></li></ul><p></p><p style="text-align: justify;"><br /></p><table border="1" cellpadding="0" cellspacing="0" class="MsoTable15List6ColorfulAccent5" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid #4BACC6 .5pt; mso-border-bottom-themecolor: accent5; mso-border-top-alt: solid #4BACC6 .5pt; mso-border-top-themecolor: accent5; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr><td style="border-bottom: 1.5pt double windowtext; border-left: none; border-right: none; border-top: 1.5pt double windowtext; padding: 0cm 5.4pt; width: 478.8pt;" valign="top" width="638"><p class="MsoNormal" style="line-height: normal; margin-top: 12pt; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;">Baca Juga :<o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-instalasi-aplikasi-geogebra.html" rel="" target="_blank">Langkah-langkah Install Aplikasi Geogebra</a><o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-praktis-membuat-kubus-di.html" rel="" target="_blank">Langkah Praktis Membuat Kubus di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-limas-di-geogebra.html" rel="" target="_blank">Cara Menggambar Limas di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-membuat-titik-dan-garis-di-geogebra.html" rel="" target="_blank">Cara Menggambar Titik dan Garis di Aplikasi Geogebra</a></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-balok-di-geogebra.html" rel="" target="_blank">Cara Menggambar Balok di Aplikasi Geogebra</a></span></b></p></td></tr></tbody></table><p style="text-align: justify;"><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-5542439818139892"></script><span style="text-align: left;"></span><!--Iklan tengah vertikal--><span style="text-align: left;"></span><ins class="adsbygoogle" data-ad-client="ca-pub-5542439818139892" data-ad-format="auto" data-ad-slot="5932457106" data-full-width-responsive="true" style="display: block; text-align: left;"></ins><script>
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</script></p><p style="-webkit-text-stroke-width: 0px; color: black; font-family: "Times New Roman"; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: justify; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Dengan cara yang sama dengan langkah-langkah diatas, kita dapat membuat prisma-prisma berikut.</span></p><p style="text-align: justify;"></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Prisma segi-6 beraturan dengan panjang rusuk alas 3 cm dan tinggi 4 cm</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjk2Z8sWplcGXL_UmyQ32bYdVypK4ZLMZgIN1XBvzcTerwwuxhfSpPtQtYNAcAEv7fP0kl3GW2rDad76IAQKfNsy44kto6V19t79TzeEm_a0oaaK6A94p8wP7b2PGotsr4m3bGHuu3Pf5I556a13TcZ11w2bbru6egvbQD-OLL79g94EyFy-jUyaVtj" style="margin-left: auto; margin-right: auto;"><img alt="Gambar Prisma Segi-6 beraturan" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjk2Z8sWplcGXL_UmyQ32bYdVypK4ZLMZgIN1XBvzcTerwwuxhfSpPtQtYNAcAEv7fP0kl3GW2rDad76IAQKfNsy44kto6V19t79TzeEm_a0oaaK6A94p8wP7b2PGotsr4m3bGHuu3Pf5I556a13TcZ11w2bbru6egvbQD-OLL79g94EyFy-jUyaVtj=w640-h360" title="Gambar Prisma Segi-6 beraturan" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 5. Prisma Segi-6 beraturan ukuran rusuk alas 3 cm dan tinggi 4 cm</td></tr></tbody></table><br /><p style="text-align: left;"><span style="font-size: medium; text-align: justify;">Untuk melihat aplikasi geogebra dari gambar prisma segi enam diatas dapat dilihat dari link <a href="https://www.geogebra.org/m/dumn2ykq" rel="nofollow" target="_blank">https://www.geogebra.org/m/dumn2ykq</a></span></p><p></p><ul style="text-align: justify;"><li><span style="font-size: medium;">Prisma segi-3 beraturan dengan panjang rusuk alas 5 cm dan tinggi 2 cm</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiaEyFB8xvOg8HW2mN8xzZJOgVPTTdslliiO80-BlF1XVS9K3Fy9EGn5ziPYNlF5Rdxzy9HR7pfxWjnN1SVOq7loVa1ptelaMYlPMFYVvO0IUzKDEGk3BPq1PkcC6CeHhEp6Zw1m0hLxw6VOr2B3mjtygJfoa-sLFy6np0TJc9gc54LPX85cUUdqlU5" style="margin-left: auto; margin-right: auto;"><img alt="Prisma Segi-3 beraturan" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiaEyFB8xvOg8HW2mN8xzZJOgVPTTdslliiO80-BlF1XVS9K3Fy9EGn5ziPYNlF5Rdxzy9HR7pfxWjnN1SVOq7loVa1ptelaMYlPMFYVvO0IUzKDEGk3BPq1PkcC6CeHhEp6Zw1m0hLxw6VOr2B3mjtygJfoa-sLFy6np0TJc9gc54LPX85cUUdqlU5=w640-h360" title="Prisma Segi-3 beraturan" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Prisma Segi-3 beraturan ukuran rusuk alas 5 cm dan tinggi 2 cm</td></tr></tbody></table><br /><p style="text-align: justify;"><span style="font-size: medium;">Untuk melihat aplikasi geogebra dari gambar prisma segi tiga diatas dapat dilihat dari link <a href="https://www.geogebra.org/m/mccxzu74" rel="nofollow" target="_blank">https://www.geogebra.org/m/mccxzu74</a></span></p><div><span style="font-size: medium;">Demikian langkah-langkah cara menggambar prisma di Geogebra. Semoga bermanfaat.</span></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-1699736261395125462022-09-09T08:26:00.010+08:002022-11-01T08:04:57.104+08:00Cara Menggambar Balok Di Geogebra<p style="text-align: justify;"><span style="font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi9bv7Av037Xmzyj2v74h8_qKogErXerwHjdKr3ifpftFNyPo5aYpCIqel0-h0YAA5mTyEQ4QqaItabbIjM5Yfsz7eYUVbZJP0YA12REwJ7kiTTLJHAQrvtXj3tT9eLH_ZaE3twKAM0fE5w5lfTusmzfD0I4Lbxe-q4tj1JblAWSEMjYOPV7h6mQY4R" style="margin-left: 1em; margin-right: 1em;"><img alt="Balok" data-original-height="472" data-original-width="739" height="127" src="https://blogger.googleusercontent.com/img/a/AVvXsEi9bv7Av037Xmzyj2v74h8_qKogErXerwHjdKr3ifpftFNyPo5aYpCIqel0-h0YAA5mTyEQ4QqaItabbIjM5Yfsz7eYUVbZJP0YA12REwJ7kiTTLJHAQrvtXj3tT9eLH_ZaE3twKAM0fE5w5lfTusmzfD0I4Lbxe-q4tj1JblAWSEMjYOPV7h6mQY4R=w200-h127" style="float: left; margin: 5px 9px;" title="Balok" width="200" /></a></span></div><span style="font-size: medium;"><div style="text-align: justify;"><b>Cara Menggambar Balok Di Geogebra</b> - Balok merupakan salah satu bentuk bangun ruang sisi datar dengan ukuran rusuk-rusuk yang berhadapan sama panjang. Ukuran balok biasa dituliskan dengan <i>p x l x t</i> dimana <i>p</i> = panjang, <i>l</i> = lebar dan <i>t</i> = tinggi. Balok àdalah bagian dari prisma.</div></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Untuk membantu pembelajaran pada materi jarak pada bangun ruang tentunya aplikasi geogebra merupakan salah satu pilihan untuk digunakan. Berikut langkah-langkah cara menggambar balok di aplikasi Geogebra Classic 6.</span></p><p style="text-align: justify;"><b><span style="font-size: medium;"><br /></span></b></p><h3 style="text-align: justify;"><b><span style="font-size: medium;">LANGKAH-LANGKAH MENGGAMBAR BALOK</span></b></h3><p style="text-align: justify;"></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Misal kita akan menggambar Balok dengan ukuran 4cm x 3cm x 5cm.</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buka aplikasi Geogebra Classic 6 versi desktop, atau Geogebra Classic online di melalui link <a href="https://geogebra.org/classic" rel="nofollow" target="_blank">https://geogebra.org/classic</a> dan buka Tampilan Grafik 3D</span></li><li style="text-align: justify;"><span style="font-size: medium;">Buatlah bidang alas dengan koordinat A(0,0,0), B(4,0,0), C(4,3,0) dan D(0,3,0). Pada kotak Masukkan ketik <b><span style="color: red;">A=(0,0,0)</span></b> lalu tekan tombol Enter. Lakukan langkah ini untuk titik B, C, dan D.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiYh39mKTemChsbLKP2-YPyu-j8QVa2gryhespZSZ2w-S5qNtBHx_BDrXs303UYgR3lwGCBF51JYPrV-3YHALgs0z_BX7CN6XshtMoPSWstRhb0qy1naUbRRhkZEIjwu2Q-mMoG9_Qi0rKGdoJmAjaDwFtNXJ0KB3BOQIIvPjS0tUgZdsdMhNU8PPy0" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Membuat Titik Alas Balok" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiYh39mKTemChsbLKP2-YPyu-j8QVa2gryhespZSZ2w-S5qNtBHx_BDrXs303UYgR3lwGCBF51JYPrV-3YHALgs0z_BX7CN6XshtMoPSWstRhb0qy1naUbRRhkZEIjwu2Q-mMoG9_Qi0rKGdoJmAjaDwFtNXJ0KB3BOQIIvPjS0tUgZdsdMhNU8PPy0=w640-h360" title="Membuat Titik Alas Balok" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Membuat Titik Alas Balok</td></tr></tbody></table><span style="font-size: medium;"><br /><br /></span><ul><li style="text-align: justify;"><span style="font-size: medium;">Buatlah poligon alas balok. Pada kotak Masukkan ketik perintah <b><span style="color: red;">poligon(A,B,C,D)</span></b>.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjlrLqc0wxZQiOj-Qtq_QqLUVqSNxNNmOHyEHKhdT8BqnWWmVkihl_UUNL3G_uoVjVH1g3rfQIYUA2j56Oq8XQglu9uNp085PkJbxtCMZ_jg9DRipD93JCZCH3_ZEFXK7lD9jrpoUWezcGc4juxL_m9cbMhb14s8mIHK-tKoMleEmH75p3U1st7rVXP" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Membuat Poligon Alas Balok" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjlrLqc0wxZQiOj-Qtq_QqLUVqSNxNNmOHyEHKhdT8BqnWWmVkihl_UUNL3G_uoVjVH1g3rfQIYUA2j56Oq8XQglu9uNp085PkJbxtCMZ_jg9DRipD93JCZCH3_ZEFXK7lD9jrpoUWezcGc4juxL_m9cbMhb14s8mIHK-tKoMleEmH75p3U1st7rVXP=w640-h360" title="Membuat Poligon Alas Balok" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2. Membuat Poligon Alas Balok</td></tr></tbody></table><span style="font-size: medium;"><br /><br /></span><ul><li style="text-align: justify;"><span style="font-size: medium;">Buatlah Balok diatas. Pada kotak Masukkan ketik perintah dengan format Prisma(poligon,tinggi).</span></li><li style="text-align: justify;"><span style="font-size: medium;">Ketik <b><span style="color: red;">Prisma(q1,5)</span></b>. q1 disesuaikan dengan nama poligon yang terbentuk dari langkah diatas.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjdvfJDcMWUOvDUKBh8xkPx8xnwCSiZ4L-pTvhwzJ24XksQiNPG0jz_9KpxO4sxElAS6EtlcO4AcBvFp6AI9zxSm1zOwq_u9jbJC1kOH7l65UJIqkowtjAA3f2dvpN_GvTvwjbxnlzGRPvYLZeXTj2FejD1xsBbxpeTB765Aya-MHCRG_aIwAlkd8Yb" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Balok 4cm x 3cm x 5cm" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjdvfJDcMWUOvDUKBh8xkPx8xnwCSiZ4L-pTvhwzJ24XksQiNPG0jz_9KpxO4sxElAS6EtlcO4AcBvFp6AI9zxSm1zOwq_u9jbJC1kOH7l65UJIqkowtjAA3f2dvpN_GvTvwjbxnlzGRPvYLZeXTj2FejD1xsBbxpeTB765Aya-MHCRG_aIwAlkd8Yb=w640-h360" title="Balok 4cm x 3cm x 5cm" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3. Balok 4cm x 3cm x 5cm</td></tr></tbody></table><span style="font-size: medium;"><br /><p></p><ul style="text-align: left;"><li style="text-align: justify;">Untuk melihat aplikasi geogebra dari balok diatas dapat dlihat melalui link <a href="https://www.geogebra.org/m/c8k66bqa" rel="nofollow" target="_blank">https://www.geogebra.org/m/c8k66bqa</a></li></ul><p></p><br /><table border="1" cellpadding="0" cellspacing="0" class="MsoTable15List6ColorfulAccent5" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid #4BACC6 .5pt; mso-border-bottom-themecolor: accent5; mso-border-top-alt: solid #4BACC6 .5pt; mso-border-top-themecolor: accent5; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr><td style="border-bottom: 1.5pt double windowtext; border-left: none; border-right: none; border-top: 1.5pt double windowtext; padding: 0cm 5.4pt; width: 478.8pt;" valign="top" width="638"><p class="MsoNormal" style="line-height: normal; margin-top: 12pt; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;">Baca Juga :<o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-instalasi-aplikasi-geogebra.html" rel="" target="_blank">Langkah-langkah Install Aplikasi Geogebra</a><o:p></o:p></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/08/langkah-praktis-membuat-kubus-di.html" rel="" target="_blank">Langkah Praktis Membuat Kubus di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; mso-ansi-language: EN-US;"><span style="font-size: medium;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-limas-di-geogebra.html" rel="" target="_blank">Cara Menggambar Limas di Aplikasi Geogebra</a></span></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-membuat-titik-dan-garis-di-geogebra.html" rel="" target="_blank">Cara Menggambar Titik dan Garis di Aplikasi Geogebra</a></span></b></p><p class="MsoNormal" style="line-height: normal; mso-yfti-cnfc: 5;"><b><span style="color: #0070c0; font-size: medium; mso-ansi-language: EN-US;"><a href="https://www.sambimatika.my.id/2022/09/cara-menggambar-prisma-di-geogebra.html" rel="" target="_blank">Cara Menggambar Prisma di Aplikasi Geogebra</a></span></b></p></td></tr></tbody></table><p style="font-size: medium; text-align: justify;"><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-5542439818139892"></script><span style="text-align: left;"></span><!--Iklan tengah vertikal--><span style="text-align: left;"></span><ins class="adsbygoogle" data-ad-client="ca-pub-5542439818139892" data-ad-format="auto" data-ad-slot="5932457106" data-full-width-responsive="true" style="display: block; text-align: left;"></ins><script>
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</script></p><p style="font-size: medium; text-align: justify;"><span style="font-size: medium;"><br /></span></p></span><div><span style="font-size: medium;">Demikian langah-langkah cara menggambar Balok di geogebra dengan ukuran 4cm x 3cm x 5cm. Semoga bermanfaat.</span><p></p></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-24824279209993541112022-09-05T20:55:00.009+08:002022-11-01T08:07:53.026+08:00Cara Membuat Titik Dan Garis di Geogebra<p style="text-align: justify;"><span style="font-size: medium;"><b>Cara Membuat Titik Dan Garis di Geogebra - </b>Pada postingan kali ini akan dibahas hal yang paling mendasar di aplikasi Geogebra yaitu bagaimana cara membuat titik dan garis. Kemampuan membuat titik dan garis pada aplikasi geogebra merupakan kemampuan dasar yang harus dikuasai jika ingin memanfaatkan aplikasi ini dalam menunjang pembelajaran. Cara membuat titik dan garis ini berlaku untuk semua jenis aplikasi geogebra, apakah untuk bidang (dimensi 2D) atau pada ruang (dimensi 3D).</span></p><p style="text-align: justify;"><span style="font-size: medium;">Perbedaan mendasar pada pembuatan titik antara bidang dan ruang adalah jika pada bidang maka titik terletak pada sumbu x dan sumbu y sehingga penulisannya seperti A(x,y). Sementara pada ruang titik terletak pada sumbu x, sumbu y dan sumbu z sehingga penulisannya menjadi A(x,y,z)</span></p><h3 style="text-align: justify;"><span style="font-size: medium;">Cara Membuat Titik Dan Garis di Geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Berikut langkah-langkah untuk membuat titik pada aplikasi Geogebra pada bidang (Dimensi 2D)</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Cara 1. Menggunakan Toolbar</b></span></p><p style="text-align: justify;"></p><ul><li style="text-align: justify;"><span style="font-size: medium;">Buka Aplikasi Geogebra, pada bahasan ini akan digunakan aplikasi Geogebra Classic online.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg08vk1e6WY8gWNulOzKjTuL1sDRaTOZ845J5NyfqIYyuZoFNddt4Ban21n7cMSrHVkEyODtjVMEbimhUfGtY7tO1voRtRaiGpyc33ljhvwwGPRfxWPtntGtKdZX9x13dXGBsDzjp2Jik5oShrjvGMeTNETnm5CqIPk1zC6VxiQfKO_PHCogOLC7PdI" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Aplikasi Geogebra Tampilan Grafik 2D" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEg08vk1e6WY8gWNulOzKjTuL1sDRaTOZ845J5NyfqIYyuZoFNddt4Ban21n7cMSrHVkEyODtjVMEbimhUfGtY7tO1voRtRaiGpyc33ljhvwwGPRfxWPtntGtKdZX9x13dXGBsDzjp2Jik5oShrjvGMeTNETnm5CqIPk1zC6VxiQfKO_PHCogOLC7PdI=w640-h360" title="Aplikasi Geogebra Tampilan Grafik 2D" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 1. Aplikasi Geogebra Tampilan Grafik 2D</span></td></tr></tbody></table><span style="font-size: medium;"><br /></span><ul><li style="text-align: justify;"><span style="font-size: medium;">Klik Toolbar <b>Titik dan huruf A </b> kemudian pilih <b>Titik Baru</b>.</span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhY5Flp_WWaWz5f-Vkgn3meZEUFnoZt3ScTJCc4GvqL49A0tSqhLNY7M0GY7DNoAaYPgYrchktioc2dD3miDGYiLeyqqWvsBUxujkeElMy4ZdcoaSG9lGsVp4B5CMXjQINfIUI5jHQANIQ_9hty95WI5J8MpOGAEoT0aI6U1fefW_giR8ojZ3bq-PQ1" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Ikon Titik Baru di Geogebra" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhY5Flp_WWaWz5f-Vkgn3meZEUFnoZt3ScTJCc4GvqL49A0tSqhLNY7M0GY7DNoAaYPgYrchktioc2dD3miDGYiLeyqqWvsBUxujkeElMy4ZdcoaSG9lGsVp4B5CMXjQINfIUI5jHQANIQ_9hty95WI5J8MpOGAEoT0aI6U1fefW_giR8ojZ3bq-PQ1=w640-h360" title="Ikon Titik Baru di Geogebra" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 2. Ikon Titik Baru di Geogebra</span></td></tr></tbody></table><span style="font-size: medium;"><br /></span><ul><li style="text-align: justify;"><span style="font-size: medium;">Pada bidang koordinat, klik pada titik yang diinginkan, maka akan terbentuk titik dengan nama mulai dari titik A dan seterusnya.</span></li></ul><p></p><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhg3V2FZcuW6963jiypj31hNmk-TKsLXJYbdvdcWpHmhhhbeY1e7cb5oAfZ2ifBAkVIRnx3Vp4OllCFTkLceTmyjI1FHcAtv61ibzuAcNN1JnaJxM1lKl8OKvcn2nKC6QMNH0KbquMlZJPL2OUkaFuU9Pu56uc3rmfayp5Xzq87_tjJcCKeW4Mj-3kB" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Titik-titik pada aplikasi Geogebra" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhg3V2FZcuW6963jiypj31hNmk-TKsLXJYbdvdcWpHmhhhbeY1e7cb5oAfZ2ifBAkVIRnx3Vp4OllCFTkLceTmyjI1FHcAtv61ibzuAcNN1JnaJxM1lKl8OKvcn2nKC6QMNH0KbquMlZJPL2OUkaFuU9Pu56uc3rmfayp5Xzq87_tjJcCKeW4Mj-3kB=w640-h360" title="Titik-titik pada aplikasi Geogebra" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 3. Gambar Titik-titik pada aplikasi Geogebra</span></td></tr></tbody></table><span style="font-size: medium;"><br /><br /></span></div><p style="text-align: left;"><b><span style="font-size: medium;">Cara 2 : Cara Manual</span></b></p><p style="text-align: left;"></p><ul style="text-align: left;"><li><span style="font-size: medium;">Misal kita mau membuat titik P(2,5) dan titik Q(-5,-2)</span></li><li><span style="font-size: medium;">Pada kotak Masukkan ketik <b><span style="color: red;">P=(2,5)</span></b> lalu tekan tombok Enter.</span></li><li><span style="font-size: medium;">Ulangi langkah diatas untuk membuat titik Q yaitu ketik <span style="color: red;"><b>Q=(-5,-2)</b></span></span></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjoHz8r7VggtlPcG27dmx19nQdSiPfQmIYKBLAgauJOPJkYZZ1AosHKziVNvPtbLEOg9g5C0Q1lQkBffYAinfevRWG6Jce5540_Xx5A3Y-PpKyC5L7ZNWDw_TAVDCRWb9RUHzHB5Pix3XeoEHGtn_o8S7ZJ3astrntEhZD6M54ugVWN6ka9Lo8eXla0" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Membuat titik secara manual" data-original-height="776" data-original-width="1366" height="364" src="https://blogger.googleusercontent.com/img/a/AVvXsEjoHz8r7VggtlPcG27dmx19nQdSiPfQmIYKBLAgauJOPJkYZZ1AosHKziVNvPtbLEOg9g5C0Q1lQkBffYAinfevRWG6Jce5540_Xx5A3Y-PpKyC5L7ZNWDw_TAVDCRWb9RUHzHB5Pix3XeoEHGtn_o8S7ZJ3astrntEhZD6M54ugVWN6ka9Lo8eXla0=w640-h364" title="Membuat titik secara manual" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 4. Membuat titik secara manual</span></td></tr></tbody></table><span style="font-size: medium;"><span><br /></span>Pada dimensi 3, cara menggambar garis, langkahnya sama dengan langkah diatas, hanya ditambah dengan koordinat pada sumbu Z sehingga titiknya menjadi misal titik <b>A(2,1,3)</b> maka pada kotak Masukkan ketik <b><span style="color: red;">A=(2,1,3)</span></b></span><p></p><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh3nIDlNc8Aq2rjZaTZ0bl9qoIyv5RBR3EfMRqpqKXaVvcUnvyTwWIAck9qleHAMDj4XPbjnqqVfXrpZMUMuN9uRjg3q-TfeDYKZ_GutgoAR4912I8XGyZkPmJOEGdGKlgZKJb6GnXYQY4GTGPR22d_aV4llCOnfamYLCAwh90doURQJDFq9RtFbjdP" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Menggambar Titik Pada Dimensi 3" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEh3nIDlNc8Aq2rjZaTZ0bl9qoIyv5RBR3EfMRqpqKXaVvcUnvyTwWIAck9qleHAMDj4XPbjnqqVfXrpZMUMuN9uRjg3q-TfeDYKZ_GutgoAR4912I8XGyZkPmJOEGdGKlgZKJb6GnXYQY4GTGPR22d_aV4llCOnfamYLCAwh90doURQJDFq9RtFbjdP=w640-h360" title="Menggambar Titik Pada Dimensi 3" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span>Gambar 5. Gambar Titik Pada Dimensi Tiga</span></td></tr></tbody></table><span style="font-size: medium;"><br /></span><p style="text-align: justify;"></p><blockquote><p style="text-align: justify;"><span style="font-size: medium;"><b>Catatan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Yang perlu diperhatikan bahwa simbol titik di geogebra selalu huruf kapital, jika bukan huruf kapital tidak terbaca sebuah titik.</b></span></p></blockquote><p style="text-align: justify;"></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><table border="1" cellpadding="0" cellspacing="0" class="MsoTable15List6ColorfulAccent5" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid #4BACC6 .5pt; mso-border-bottom-themecolor: accent5; mso-border-top-alt: solid #4BACC6 .5pt; mso-border-top-themecolor: accent5; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
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<p style="text-align: justify;"><span style="font-size: medium;"><span>Selanjutnya b</span><span>erikut langkah-langkah untuk membuat garis pada aplikasi Geogebra pada bidang (Dimensi 2D)</span></span></p><h3 style="text-align: justify;"><span style="font-size: medium;"><span>Langkah-langkah membuat garis pada aplikasi Geogebra pada bidang (Dimensi 2D)</span></span></h3><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">Pada postingan ini akan dibahas empat perintah pada garis yaitu :</span></p><p style="text-align: justify;"></p><ol><li style="text-align: justify;"><span style="font-size: medium;">Perintah Garis(titik-1,titik-2) yaitu membuat garis tak hinga panjangnya</span></li><li style="text-align: justify;"><span style="font-size: medium;">Perintah Ruasgaris(titik-1,titik-2) yaitu membuat garis dari titik-1 sampai titik-2</span></li><li style="text-align: justify;"><span style="font-size: medium;">Perintah Sinar(titik-1,titik-2) yaitu membuat garis dari titik-1 melalui titik-2 sampai tak hingga</span></li><li style="text-align: justify;"><span style="font-size: medium;">Perintah ruas garis dengan panjang tetap</span></li></ol><span style="font-size: medium;"><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Cara 1</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Langkah-langkah membuat garis tak hingga panjangnya</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">1. Klik toolbar garis, dan klik Garis yang melalui dua titik</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhE-q59z6XTPSPjRxVqkVJ_Hoku1I8UMJaXU13jsGLXHTxx0u8GVb3Lx--0duYrInFgHkJIQo7MJkrJFawIBq2XeLGjXVBG_nkxqckHhNrGW9RLygViSQKanbkwp1wqhzztoeMc9h5rrU2Po_4def1jXStIQyi0Ygy59aijJBKhwO2Y-G6MmCZR6oZ5" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar garis yang melalui dua titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhE-q59z6XTPSPjRxVqkVJ_Hoku1I8UMJaXU13jsGLXHTxx0u8GVb3Lx--0duYrInFgHkJIQo7MJkrJFawIBq2XeLGjXVBG_nkxqckHhNrGW9RLygViSQKanbkwp1wqhzztoeMc9h5rrU2Po_4def1jXStIQyi0Ygy59aijJBKhwO2Y-G6MmCZR6oZ5=w640-h360" title="Toolbar garis yang melalui dua titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 6. Toolbar garis yang melalui dua titik</td></tr></tbody></table><span style="font-size: medium;"><br /><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">2. Pada bidang kartesius klik titik-1 dilanjutkan dengan klik titik-2 <b>(Perhatikan garis AB)</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjSoP3quup-uFna45G40Yavw8Zfoh-7l3rZhD2PS1OLcca5NEIAWnYciIGqnk2H35tV_Rfi4FBQ3c-AZcMvaIiZXy-1o90D_RlwAwHRoG6K2bAXAESGXPOKIaA4kYR_AJzq8ZlC21W5QrCL0rLILy5zfu7lmHRs3uJ2MeiRJHHk8m5FBDTt-fZccHwm" style="margin-left: auto; margin-right: auto;"><img alt="Garis yang melalui dua titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjSoP3quup-uFna45G40Yavw8Zfoh-7l3rZhD2PS1OLcca5NEIAWnYciIGqnk2H35tV_Rfi4FBQ3c-AZcMvaIiZXy-1o90D_RlwAwHRoG6K2bAXAESGXPOKIaA4kYR_AJzq8ZlC21W5QrCL0rLILy5zfu7lmHRs3uJ2MeiRJHHk8m5FBDTt-fZccHwm=w640-h360" title="Garis yang melalui dua titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 7. Garis yang melalui dua titik</td></tr></tbody></table><span style="font-size: medium;"><br /><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"><b>Langkah-langkah membuat ruas garis</b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">1. Klik toolbar garis, dan klik Ruas garis diantara dua titik</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg4R91sQ1UkTl4mZ7Z7zd22CR6WS28wb_2Uu3-SBzD_NtT-8UEduQy25RQJPOkR-C-kplT0WkGcyxC2oUQ5cUjaeFxKtFoY-r_OemKDccF48po07kDNSuU8Wj5POKs-4PyTSI6jo-ic7XHeaAqGIWeuePoJ0vyPEFiY6sbV2Rc-QGR9ChlAvkuoah4U" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar Ruas garis diantara dua titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEg4R91sQ1UkTl4mZ7Z7zd22CR6WS28wb_2Uu3-SBzD_NtT-8UEduQy25RQJPOkR-C-kplT0WkGcyxC2oUQ5cUjaeFxKtFoY-r_OemKDccF48po07kDNSuU8Wj5POKs-4PyTSI6jo-ic7XHeaAqGIWeuePoJ0vyPEFiY6sbV2Rc-QGR9ChlAvkuoah4U=w640-h360" title="Toolbar Ruas garis diantara dua titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 8. Toolbar Ruas garis diantara dua titik</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br /><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">2. Pada bidang kartesius klik titik-1 dilanjutkan dengan klik titik-2 <b>(Perharikan garis CD)</b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhX2b35ScpU6DSHhj_2xRIMitiaUWjnD21P0AZgkkoQpfCLhljVHwRf0cKjF8OPr9-vXG7T0tT8qez6Qk1Q5MZD3ams42NIFJV5JHkDLdsh5lGmaMX8q17GKx0cB__2JehP9-trO7QArLWhPilcGYy57Lf1uzC2OhbI2f1Wa-jPbpU5n5GPDNYrgEyb" style="margin-left: auto; margin-right: auto;"><img alt="Ruas garis diantara dua titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEhX2b35ScpU6DSHhj_2xRIMitiaUWjnD21P0AZgkkoQpfCLhljVHwRf0cKjF8OPr9-vXG7T0tT8qez6Qk1Q5MZD3ams42NIFJV5JHkDLdsh5lGmaMX8q17GKx0cB__2JehP9-trO7QArLWhPilcGYy57Lf1uzC2OhbI2f1Wa-jPbpU5n5GPDNYrgEyb=w640-h360" title="Ruas garis diantara dua titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 9. Ruas garis diantara dua titik</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br /><br /></span></div><div><span style="font-size: medium; text-align: justify;"><b>Langkah-langkah membuat ruas garis dengan panjang tetap</b></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">1. Klik ikon garis dan pilih Ruas garis dengan panjang tetap</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgg5g_vpQTIFckWpuYVdOeAeLEby6aUC3QmUV__Mb1nUvVrtcjtS8okRzo0cRWW6sgTK7YXEKZmMguqfnRde1n0Q3JMF_mmEHNC_91lJx-rAbHxwMCo6peU7oFpSjZFR9YfreLQyf-os4gXTNc6KgZc1IeLdrJd-c6MctzP4jJHZ-bJT3WrNEeb6KEE" style="margin-left: auto; margin-right: auto;"><img alt="Toolbar ruas garis dengan panjang tetap" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgg5g_vpQTIFckWpuYVdOeAeLEby6aUC3QmUV__Mb1nUvVrtcjtS8okRzo0cRWW6sgTK7YXEKZmMguqfnRde1n0Q3JMF_mmEHNC_91lJx-rAbHxwMCo6peU7oFpSjZFR9YfreLQyf-os4gXTNc6KgZc1IeLdrJd-c6MctzP4jJHZ-bJT3WrNEeb6KEE=w640-h360" title="Toolbar ruas garis dengan panjang tetap" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 10. Toolbar ruas garis dengan panjang tetap</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br /><br /></span></div><div><span style="font-size: medium; text-align: justify;">2. Klik titik-1, kemudian akan muncul kotak untuk memasukkan panjang garis yang ingin dibuat lalu klik tombok OK</span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgbGxoH54K1Daf20cF3tRnxX1gAifnWKYaYLqt3MCQf24cWJDH-YqfGvOt7sH9ij6EXsCyBRvZZxL08DTnKUOlAGnB-hQTbCgUQKnrv2J5oy6cGDC2ZmTUkSW8bw5JNDSMJB_jg7MZ7WDDyjvJ4Cl0U0SkuTm_7yBpXLVOME-rFMZqDTbS8CvuK-55L" style="margin-left: auto; margin-right: auto;"><img alt="Input Panjang Ruas Garis" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgbGxoH54K1Daf20cF3tRnxX1gAifnWKYaYLqt3MCQf24cWJDH-YqfGvOt7sH9ij6EXsCyBRvZZxL08DTnKUOlAGnB-hQTbCgUQKnrv2J5oy6cGDC2ZmTUkSW8bw5JNDSMJB_jg7MZ7WDDyjvJ4Cl0U0SkuTm_7yBpXLVOME-rFMZqDTbS8CvuK-55L=w640-h360" title="Input Panjang Ruas Garis" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 11. Input Panjang Ruas Garis</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br /><br /></span></div><div><span style="font-size: medium; text-align: justify;">3. Hasilnya seperti ini. <b>(Perhatikan garis EF)</b></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjKBEyv9_KZ-SgfHOa2igXdA6sRJl9KLlC4mYlAbgi8ft7m5kE9dzM2vAwSESgmE1ouZRzIbhlUDZjFUMvL8ErgJxKZkoS6-oBjw2qDau9qIgLT8joWjYWUc9qB3EbLDW7Vk01l9RhB0ee924we2EZ0PHM3B0FGi81BlWA7GN1RD4LOWliN6Ge5cy3Q" style="margin-left: auto; margin-right: auto;"><img alt="Ruas Garis antara Dua Titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjKBEyv9_KZ-SgfHOa2igXdA6sRJl9KLlC4mYlAbgi8ft7m5kE9dzM2vAwSESgmE1ouZRzIbhlUDZjFUMvL8ErgJxKZkoS6-oBjw2qDau9qIgLT8joWjYWUc9qB3EbLDW7Vk01l9RhB0ee924we2EZ0PHM3B0FGi81BlWA7GN1RD4LOWliN6Ge5cy3Q=w640-h360" title="Ruas Garis antara Dua Titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 12. Ruas Garis antara Dua Titik</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br /><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"><b>Langkah-langkah membuat sinar garis</b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">1. Klik Toolbar garis dan klik Sinar melalui dua titik</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgOlnyHMYiQev6BJAsjA_JTAhHsAkh1n42mNxaCPOswga_FAp-63j91dRXOutWktbRfU7vozsD3i9Ge7zmBdRbKL4bij4M3F5xsMP5WQ_OqQ3mKhWJNPpYbptXiht5-sCMMpb02pSiYXmNcFLKxjfEPYm_TjkxrPEkHnMqoEgw2HVKuGgxuOMtM2Dl8" style="margin-left: auto; margin-right: auto;"><img alt="Sinar melalui dua titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEgOlnyHMYiQev6BJAsjA_JTAhHsAkh1n42mNxaCPOswga_FAp-63j91dRXOutWktbRfU7vozsD3i9Ge7zmBdRbKL4bij4M3F5xsMP5WQ_OqQ3mKhWJNPpYbptXiht5-sCMMpb02pSiYXmNcFLKxjfEPYm_TjkxrPEkHnMqoEgw2HVKuGgxuOMtM2Dl8=w640-h360" title="Sinar melalui dua titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 13. Toolbar Sinar melalui dua titik</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br /><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">2. Pada bidang kartesius klik titik-1 dilanjutkan dengan titik-2 <b>(Perhatikan garis GH)</b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiGrjJyWHnm3gGQu5pI5CZnA-j-EooDfrXnEcaf7vEDF9yimZVnotmVMAAJIXfnkaQteTsBa1Y8V3FLQ8B3HLAEBxP8IuWED_Kg-GETNmkDs8MkruUsPtBGmQfLFS2kbqE7TVkJLJyFQL3ir9LXs-gz_89V4EanHGL6u5Np0WOR4lPC-BFTFfQaWegV" style="margin-left: auto; margin-right: auto;"><img alt="Sinar melalui dua titik" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEiGrjJyWHnm3gGQu5pI5CZnA-j-EooDfrXnEcaf7vEDF9yimZVnotmVMAAJIXfnkaQteTsBa1Y8V3FLQ8B3HLAEBxP8IuWED_Kg-GETNmkDs8MkruUsPtBGmQfLFS2kbqE7TVkJLJyFQL3ir9LXs-gz_89V4EanHGL6u5Np0WOR4lPC-BFTFfQaWegV=w640-h360" title="Sinar melalui dua titik" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 14. Sinar melalui dua titik</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br />Untuk melihat aplikasi geogebra dari titik dan garis diatas dapat dilihar melalui link <a href="https://www.geogebra.org/m/zhsmqkx5" rel="nofollow" target="_blank">https://www.geogebra.org/m/zhsmqkx5</a><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"><b>Cara 2. Cara Manual</b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">1. Buatlah dokumen baru</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">2. Buatlah titik-titik secara menual Misal titik A, B, C, D, E, F dan G dengan koordinat diserahkan ke pembaca</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">3. Untuk membuat garis pada kotak masukkan ketik <b><span style="color: red;">Garis(A,B)</span></b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">4. Untuk membuat Ruas garis ketik <b><span style="color: red;">Ruasgaris(C,D)</span></b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">5. Untuk membuat Sinar Garis ketik <b><span style="color: red;">Sinar(E,F)</span></b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">6. Untuk Membuat ruas garis dengan panjang tertentu ketik <b><span style="color: red;">Ruasgaris(G,6)</span></b></span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;">Hasilnya seperti gambar berikut</span></p><p style="text-align: justify;"><span style="font-size: medium; text-align: justify;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjK5aS_Cguv5Ny1Ietv3L1U_kvBRGogFrB9XL-T96-Sym6o9jzdU264W2lG63RmWwabEWUZdouPPZxs9am-CNCP8ciFExwA93iJ-0UH7T4z737-cKanzW6ivwjY7HSbGZrzQDNs9dJNyRKdVJZLfBqglgXxl3QMqu9W152CSn9mg6N8x5vNoy8Osft7" style="margin-left: auto; margin-right: auto;"><img alt="Membuat Garis dengan Cara Manual" data-original-height="768" data-original-width="1366" height="360" src="https://blogger.googleusercontent.com/img/a/AVvXsEjK5aS_Cguv5Ny1Ietv3L1U_kvBRGogFrB9XL-T96-Sym6o9jzdU264W2lG63RmWwabEWUZdouPPZxs9am-CNCP8ciFExwA93iJ-0UH7T4z737-cKanzW6ivwjY7HSbGZrzQDNs9dJNyRKdVJZLfBqglgXxl3QMqu9W152CSn9mg6N8x5vNoy8Osft7=w640-h360" title="Membuat Garis dengan Cara Manual" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 15. Membuat Garis dengan Cara Manual</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium; text-align: justify;"></span></div><span style="font-size: medium; text-align: justify;"><br /><br /></span><p></p><p style="text-align: justify;"><span style="font-size: medium;">Demikian pembahasan cara membuat titik dan garis di geogebra, semoga bermanfaat.</span></p></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-7205043011098257996.post-81073478498025497972022-09-04T19:18:00.005+08:002022-11-01T08:09:18.741+08:00Cara Menggambar Limas di Geogebra<p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjF9GLtYlO4MXBho1rDosNgEL4k2yiH06baWgIneg9p9hjXvoePP-0KlCiWH_-9ZdKyAI0MtOQyBlDPm6I3Eq33pFRbIUFugYjf8RbnQNDDPeDc0q4l9pUdVAaJCkGqQOm1Is8km85-fUIhyNMAdU7se0_282hhyANdbPWnunxbAnvaF_xBpBXPknfa" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Limas" data-original-height="555" data-original-width="929" height="119" src="https://blogger.googleusercontent.com/img/a/AVvXsEjF9GLtYlO4MXBho1rDosNgEL4k2yiH06baWgIneg9p9hjXvoePP-0KlCiWH_-9ZdKyAI0MtOQyBlDPm6I3Eq33pFRbIUFugYjf8RbnQNDDPeDc0q4l9pUdVAaJCkGqQOm1Is8km85-fUIhyNMAdU7se0_282hhyANdbPWnunxbAnvaF_xBpBXPknfa=w200-h119" style="float: left; margin: 5px 9px;" title="Limas" width="200" /></span></a></div><div style="text-align: justify;"><span style="font-size: medium;"><b>Cara Menggambar Limas di Geogebra - </b>Pada bahasan sebelum ini kita sudah membahas cara menggambar Kubus menggunanakan aplikasi Geogebra. Pada bahasan kali ini kita akan membahas cara menggambar limas di Geogebra. Pada bahasan ini saya menggunakan Aplikasi Geogebra versi online yang sama dengan Aplikasi Geogebra Classic 6.</span></div><p></p><h3 style="text-align: justify;"><span style="font-size: medium;">Langkah-Langkah Menggambar Limas di Geogebra</span></h3><p style="text-align: justify;"><span style="font-size: medium;">Berikut langkah-langkah cara menggambar limas menggunakan aplikasi Geogebra.</span></p><ul style="text-align: justify;"><li><span style="font-size: medium;">Buka aplikasi Geogebra online melalui link<a href="https://www.geogebra.org/classic" rel="nofollow" target="_blank"> https://www.geogebra.org/classic</a> dan pilih tampilan Grafik 3D.<br /></span></li></ul><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijV-AZIuUG6iu0BBZROGg-41ncEg_QsDRkOAmVEJ5bFYSPcQP8crwZYU69r5hxGGsKiY7LchVN9rYCrQowu2KhF5W8lDiOjxJc2p9aCLJ8d7DrcOmG6ru0VjYWqo96ZgFJawRS4M8Ra5cOt8pGRyp3DugEAbt4VLicKw9NeLHDGCMBHOZE0yHxCHmV/s1366/geogebra%201.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Geogebra Classic Tampilan Grafik 3D" border="0" data-original-height="776" data-original-width="1366" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijV-AZIuUG6iu0BBZROGg-41ncEg_QsDRkOAmVEJ5bFYSPcQP8crwZYU69r5hxGGsKiY7LchVN9rYCrQowu2KhF5W8lDiOjxJc2p9aCLJ8d7DrcOmG6ru0VjYWqo96ZgFJawRS4M8Ra5cOt8pGRyp3DugEAbt4VLicKw9NeLHDGCMBHOZE0yHxCHmV/w640-h364/geogebra%201.png" title="Geogebra Classic Tampilan Grafik 3D" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 1. Geogebra Classic Tampilan Grafik 3D</td></tr></tbody></table><p></p><span style="font-size: medium;"><br /></span><ul style="text-align: left;"><li style="text-align: justify;"><span style="text-align: left;"><span style="font-size: medium;">Misal kita mau menggambar Limas beraturan dengan panjang rusuk alas 4 cm dan tinggi 5 cm.</span></span></li><li><span style="font-size: medium;">Buat titik alas limas, A(0,0,0), B(4,0,0), C(4,4,0), D(0,4,0)</span></li><li style="text-align: justify;"><span style="font-size: medium;">Pada kotak Masukkan ketik <b><span style="color: red;">A=(0,0,0)</span></b> lalu tekan tombol enter, begitu selanjutnya untuk titik B, C dan D.</span></li></ul><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCMxTIinEBjuiM8DgTAhrx47Ui_EkdsMZrAR2dJe9Y1n1fcNbgEbfAhWVcIntpKNv7DRY-5oFp0paahOkTxqNyZf53KDLQsoI0tD9o52ZfmZjW74KImzbPqjr9IwOWN6fuS-KU8AhtauoMIea3ZucyyItV6ccKoplbpYWduPfZcy7SZRwRXEiNHr56/s1366/geogebra%202.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Membuat titik pada Geogebra" border="0" data-original-height="776" data-original-width="1366" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCMxTIinEBjuiM8DgTAhrx47Ui_EkdsMZrAR2dJe9Y1n1fcNbgEbfAhWVcIntpKNv7DRY-5oFp0paahOkTxqNyZf53KDLQsoI0tD9o52ZfmZjW74KImzbPqjr9IwOWN6fuS-KU8AhtauoMIea3ZucyyItV6ccKoplbpYWduPfZcy7SZRwRXEiNHr56/w640-h364/geogebra%202.png" title="Membuat titik pada Geogebra" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 2 Membuat Titik Alas Limas Beraturan</td></tr></tbody></table><br /><p></p><div style="text-align: justify;"><ul><li><span style="font-size: medium;">Untuk Menggambar alas limas, pada kotak Masukkan ketik <b><span style="color: red;">Poligon(A,B,C,D)</span></b> lalu tekan tombol enter</span></li></ul></div><p></p><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2Slovwv52PUCmg6InovdMi3u9dqJKW_SPZXCpoEBISEvtUKg5oQmlS2iKtpscrGVIoI7znEOHZfyZF_DfrNYTxixv7tQoQsfXnFxQfs1WQmnLLjJ-SgoRTO3bbxL3kGJV8DdY10yPlNBH3C6avEurnMF4TKjFUrU0sbrxB7LWLK6HIlFibs6ozEFd/s1366/geogebra%203.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Menggambar Alas Limas Beraturan" border="0" data-original-height="776" data-original-width="1366" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2Slovwv52PUCmg6InovdMi3u9dqJKW_SPZXCpoEBISEvtUKg5oQmlS2iKtpscrGVIoI7znEOHZfyZF_DfrNYTxixv7tQoQsfXnFxQfs1WQmnLLjJ-SgoRTO3bbxL3kGJV8DdY10yPlNBH3C6avEurnMF4TKjFUrU0sbrxB7LWLK6HIlFibs6ozEFd/w640-h364/geogebra%203.png" title="Menggambar Alas Limas Beraturan" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 3 Menggambar Alas Limas Beraturan</td></tr></tbody></table><p></p><div style="text-align: justify;"><br /><ul><li><span style="font-size: medium;">Untuk menggambar limas, pada kotak Masukkan ketik <b><span style="color: red;">Piramida(q1,5)</span></b> lalu tekan tombol Enter. q1 = kode fungsi alas limas (lihat pada bagian akhir di kotak masukkan), 5 = tinggi limas.</span></li></ul></div><p style="text-align: left;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYHghUecP91YRjVoLXwQoFuKNQ-0AA3bqkS3wx_sfYhLARpTxWT5DiMb6urxKj5LlWJ4iLMu5Ub0DJX_m0Gj-F56gEfi72W4A-s7DvkFZ14ypNHDIeGH0NMPprnwdnjJtAPVnd6SU5aoZcBJgKTbG97rS2wYKuTdwvzzyB24SnvM3dOCqTy-UG5YO-/s1366/geogebra%204.png" style="margin-left: auto; margin-right: auto;"><span style="font-size: medium;"><img alt="Menggambar Limas Beraturan" border="0" data-original-height="776" data-original-width="1366" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYHghUecP91YRjVoLXwQoFuKNQ-0AA3bqkS3wx_sfYhLARpTxWT5DiMb6urxKj5LlWJ4iLMu5Ub0DJX_m0Gj-F56gEfi72W4A-s7DvkFZ14ypNHDIeGH0NMPprnwdnjJtAPVnd6SU5aoZcBJgKTbG97rS2wYKuTdwvzzyB24SnvM3dOCqTy-UG5YO-/w640-h364/geogebra%204.png" title="Menggambar Limas Beraturan" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gambar 4. Gambar Limas Beraturan panjang rusuk alas 4 dan tinggi 5</td></tr></tbody></table><p></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Untuk melihat aplikasi geogebra dari limas diatas dapat dilihat melalui link <a href="https://www.geogebra.org/m/xqnbjxsn" rel="nofollow" target="_blank">https://www.geogebra.org/m/xqnbjxsn</a></span></p><p style="text-align: justify;"><span style="font-size: medium;">Demikian cara menggambar limas menggunakan aplikasi Geogebra Classic 6. Semoga bermanfaat dan selamat mencoba</span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708